CN113515519A - Training method, device, device and storage medium for graph structure estimation model - Google Patents

Abstract

Embodiments of the present invention disclose a training method, device, device and storage medium for a graph structure estimation model, wherein the method includes: acquiring an initial graph and label information corresponding to the initial graph; the initial graph includes multiple nodes, and the label information is used to indicate The category of the target node in the initial graph, and the target node is any one or more of the multiple nodes in the initial graph; call the graph prediction model included in the graph structure estimation model to perform prediction processing on the initial graph, and obtain the observation information corresponding to the initial graph; call The graph estimator included in the graph structure estimation model performs estimation processing based on label information and observation information to obtain an estimated graph; and calls the graph prediction model to perform prediction processing on the estimated graph to obtain the prediction information corresponding to the estimated graph; based on the prediction information corresponding to the estimated graph and The label information optimizes the graph prediction model. By adopting the embodiments of the present invention, the accuracy of the graph structure estimation model can be provided.

Description

Training method, device, equipment and storage medium for graph structure estimation model

technical field

The present application relates to the field of graph processing, and in particular, to a training method, apparatus, device and storage medium for a graph structure estimation model.

Background technique

Graphs are everywhere, from chemical and bioinformatics research to image and social network analysis. The so-called graph is the most direct tool used to describe the community relationship chain. It consists of nodes and edges. The nodes represent the objects in the community, and the edges represent the closeness of the connection between the two objects. Due to the ubiquity of graphs, it is especially important to learn efficient representations of graphs and apply them to downstream tasks. Recently, graph processing models for graph representation learning have attracted widespread attention, such as Graph Neural Networks (GNN) model, Graph Convolutional Network (Graph Convolutional Network) GCN model, etc. The model roughly follows a recursive message passing mechanism, i.e., neighborhood information is aggregated and passed to neighbors.

Currently used graph processing models are usually obtained by training based on graph training samples. During training, it is generally assumed that the graph structure of the graph training samples is correct and conforms to the model properties of the graph processing model. However, the graph training samples are generally extracted from complex interactive systems in practical applications. Due to some errors in the interactive system of practical applications, there may be some missing, meaningless, or even wrong edges in the graph training samples, which leads to the graph training samples and GNN. The properties do not match, thus affecting the accuracy of the GNN model. Therefore, in the field of graph processing, how to train the model for graph processing to improve the accuracy of the model has become a hot research issue.

SUMMARY OF THE INVENTION

The embodiments of the present invention provide a training method, apparatus, device and storage medium for a graph structure estimation model, which can improve the accuracy of the graph structure estimation model.

On the one hand, an embodiment of the present invention provides a method for training a graph structure estimation model, including:

Obtain the initial graph and the label information corresponding to the initial graph; the initial graph includes multiple nodes, and the label information is used to indicate the category to which the target node in the initial graph belongs, and the target node is a plurality of nodes in the initial graph. any one or more of the nodes;

Calling the graph prediction model included in the graph structure estimation model to perform prediction processing on the initial graph to obtain observation information corresponding to the initial graph;

Calling the graph estimator included in the graph structure estimation model to perform estimation processing based on the label information and the observation information to obtain an estimated graph; and calling the graph prediction model to perform prediction processing on the estimated graph to obtain the estimated graph Corresponding prediction information, where the prediction information corresponding to the estimation graph is used to indicate the category to which each node in the estimation graph belongs;

The graph prediction model is optimized based on the prediction information corresponding to the estimated graph and the label information.

On the one hand, an embodiment of the present invention also provides a training device for a graph structure estimation model, including:

an obtaining unit, configured to obtain an initial graph and label information corresponding to the initial graph; the initial graph includes a plurality of nodes, and the label information is used to indicate the category to which the target node in the initial graph belongs, and the target node is the any one or more of the multiple nodes of the initial graph;

a processing unit, configured to call the graph prediction model included in the graph structure estimation model to perform prediction processing on the initial graph to obtain observation information corresponding to the initial graph;

The processing unit is further configured to call a graph estimator included in the graph structure estimation model to perform estimation processing based on the label information and the observation information to obtain an estimated graph; and call the graph prediction model to perform an estimation on the estimated graph. Prediction processing to obtain prediction information corresponding to the estimation graph, where the prediction information corresponding to the estimation graph is used to indicate the category to which each node in the estimation graph belongs;

The processing unit is further configured to optimize the graph prediction model based on the prediction information corresponding to the estimation graph and the label information.

On the one hand, an embodiment of the present invention provides a training device for a graph structure estimation model, which is characterized by comprising: a processor adapted to implement one or more computer programs; and a computer storage medium, which stores one or more computer programs. Computer programs, one or more of which are adapted to be loaded and executed by a processor:

Obtain the initial graph and the label information corresponding to the initial graph; the initial graph includes multiple nodes, and the label information is used to indicate the category to which the target node in the initial graph belongs, and the target node is a plurality of nodes in the initial graph. Any one or more of the nodes; call the graph prediction model included in the graph structure estimation model to perform prediction processing on the initial graph, and obtain the observation information corresponding to the initial graph; call the graph estimator included in the graph structure estimation model Perform estimation processing based on the label information and the observation information to obtain an estimated graph; and call the graph prediction model to perform prediction processing on the estimated graph to obtain prediction information corresponding to the estimated graph, and the prediction corresponding to the estimated graph The information is used to indicate the category to which each node in the estimation graph belongs; the graph prediction model is optimized based on the prediction information corresponding to the estimation graph and the label information.

On the one hand, an embodiment of the present invention provides a computer storage medium, where the computer storage medium stores a computer program, and when the computer program is executed by a processor, is used to execute:

Obtain the initial graph and the label information corresponding to the initial graph; the initial graph includes multiple nodes, and the label information is used to indicate the category to which the target node in the initial graph belongs, and the target node is a plurality of nodes in the initial graph. Any one or more of the nodes; call the graph prediction model included in the graph structure estimation model to perform prediction processing on the initial graph, and obtain the observation information corresponding to the initial graph; call the graph estimator included in the graph structure estimation model Perform estimation processing based on the label information and the observation information to obtain an estimated graph; and call the graph prediction model to perform prediction processing on the estimated graph to obtain prediction information corresponding to the estimated graph, and the prediction corresponding to the estimated graph The information is used to indicate the category to which each node in the estimation graph belongs; the graph prediction model is optimized based on the prediction information corresponding to the estimation graph and the label information.

On the one hand, an embodiment of the present invention provides a computer program product or a computer program, the computer program product includes a computer program, and the computer program is stored in a computer storage medium; the processor of the model processing device reads the computer program from the computer storage medium, The processor executes the computer program, causing the model processing device to execute:

Obtain the initial graph and the label information corresponding to the initial graph; the initial graph includes multiple nodes, and the label information is used to indicate the category to which the target node in the initial graph belongs, and the target node is a plurality of nodes in the initial graph. Any one or more of the nodes; call the graph prediction model included in the graph structure estimation model to perform prediction processing on the initial graph, and obtain the observation information corresponding to the initial graph; call the graph estimator included in the graph structure estimation model Perform estimation processing based on the label information and the observation information to obtain an estimated graph; and call the graph prediction model to perform prediction processing on the estimated graph to obtain prediction information corresponding to the estimated graph, and the prediction corresponding to the estimated graph The information is used to indicate the category to which each node in the estimation graph belongs; the graph prediction model is optimized based on the prediction information corresponding to the estimation graph and the label information.

In the embodiment of the present invention, a new model for processing graphs, that is, a graph structure estimation model is proposed, and the graph structure estimation model is composed of a graph prediction model and a graph estimator. In the process of optimizing the graph structure estimation model, the graph prediction model in the graph structure estimation model can be invoked to perform prediction processing on the initial graph to obtain observation information corresponding to the initial graph, where the observation information includes the corresponding initial graph. The prediction information of Prediction information; optimize the graph prediction model based on the prediction information corresponding to the estimated graph and the label information corresponding to the initial graph.

It can be seen from the above process that the optimization of the graph prediction model is not only based on the initial graph and the label information corresponding to the initial graph, but also optimizes the graph prediction model based on the estimated graph. The estimated graph is obtained by estimating the observation information obtained by the graph estimator predicting the initial graph based on the graph prediction model. In other words, the estimated graph is obtained by observing the initial graph from the perspective of the graph prediction model, that is to say, the estimated graph better matches the properties of the graph prediction model than the initial graph, which is more in line with the graph structure. Estimate the properties of the model. Therefore, optimizing the training of the graph prediction model based on the estimated graph can improve the accuracy of the graph prediction model, thereby improving the accuracy of the graph structure estimation model.

Description of drawings

In order to explain the technical solutions of the embodiments of the present invention more clearly, the following briefly introduces the accompanying drawings used in the description of the embodiments. Obviously, the drawings in the following description are some embodiments of the present invention, which are of great significance to the art For those of ordinary skill, other drawings can also be obtained from these drawings without any creative effort.

1 is a schematic diagram of a diagram of a social network provided by an embodiment of the present invention;

2 is a schematic diagram of a graph structure estimation model provided by an embodiment of the present invention;

3 is a schematic flowchart of a training method for a graph structure estimation model provided by an embodiment of the present invention;

4a is a schematic diagram of an initial diagram provided by an embodiment of the present invention;

4b is a schematic diagram of an adjacency matrix corresponding to an initial graph provided by an embodiment of the present invention;

5 is a schematic flowchart of another training processing method for a graph structure estimation model provided by an embodiment of the present invention;

6 is a schematic diagram of determining an estimated adjacency matrix provided by an embodiment of the present invention;

7 is a schematic diagram of training of a graph structure estimation model provided by an embodiment of the present invention;

8a is a box plot of the predicted values of each node by a GCN model and a GEN model provided by an embodiment of the present invention;

Fig. 8b is the variation curve of true-positive probability and false-positive probability on two different data sets of a kind of GEN model that the embodiment of the present invention provides;

9a is a schematic diagram of the accuracy curve of a GEN model and other graph processing models provided by an embodiment of the present invention;

FIG. 9b is a visualized initial graph and estimation graph provided by an embodiment of the present invention;

9c is a probability matrix between communities of an initial graph and an estimated graph provided by an embodiment of the present invention;

9d is a relationship diagram between a first quantity and a node pair provided by an embodiment of the present invention;

Fig. 9e is the normalized histogram of the edge confidence of a kind of different communities provided by the embodiment of the present invention on the training data set, the verification data set and the test data set for training the GEN model;

10 is a schematic structural diagram of a training device for a graph structure estimation model provided by an embodiment of the present invention;

FIG. 11 is a schematic structural diagram of a training device for a graph structure estimation model provided by an embodiment of the present invention.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

A graph is the most direct tool used to describe the community relationship chain. It consists of nodes and edges. Nodes represent objects in the community, and edges represent the degree of connection between two objects. In a narrow sense, a community has a certain interactive relationship and a common cultural tie. A community and its interactive area formed by interrelated people in a certain field. For example, a karate club can be regarded as a community, or a company. It can be thought of as a community; in a broad sense, a community can include social networks, biological networks, and infrastructure networks such as energy, transportation, the Internet, and communications. Graphs can include directed graphs and undirected graphs. Each edge in a directed graph is directed, and each edge in an undirected graph is undirected.

For example, referring to FIG. 1 , which is a graph of a social network provided by an embodiment of the present invention, the graph may be a directed graph. The objects of the social network may include users, schools, and companies, and these objects are used as nodes of the graph; if there is an association between two objects, there is an edge between the two objects, for example, user 101 and user 102 are friends. , then there is an edge 100 between the user 101 and the user 102 ; for another example, if the user 101 works in the company 103 , then there is an edge 104 between the user 101 and the company 103 . By analogy, the graph of the social network shown in Figure 1 is obtained.

In today's society, due to the ubiquity of graphs, efficient and accurate processing of graphs is especially important for downstream tasks. Based on the continuous development of deep learning, a graph processing model for graph processing emerges as the times require. The graph processing model in the prior art refers to a model constructed based on a graph neural network (GNN). In the past few years, the graph neural network GNN has achieved great success in solving graph machine learning problems. Most of the current graph neural network models can be divided into two categories, one is the graph processing model based on the spectral method, Another category is graph processing models based on spatial methods.

Spectral-based graph processing models use graph theory to learn node representations in graphs. For example, some studies use the Fourier basis to propose a spectral domain-based convolution network extension on graphs; other studies use graph convolution based on chebyshev polynomials to eliminate computationally expensive Laplacian feature decomposition; , a typical spectral-based graph neural network is the graph convolutional network GCN, which further simplifies the chebyshev polynomial-based graph convolution by using its first-order approximation.

Graph processing models based on spatial methods define graph convolutions directly in the spatial domain to aggregate and transform local information. For example, some studies learn to aggregate neighbor information by sampling and aggregating it; some studies assign different edge weights according to node features during aggregation; others perform importance sampling at each layer to improve efficiency to sample a fixed number of nodes.

Among the above graph processing models, all graph processing models are obtained by training a large number of graph training samples and the label information corresponding to the graph training samples. In the training process, it is assumed that each graph training sample is correct. However, graph training samples are all from complex interactive systems. In practical applications, various interactive systems usually contain uncertainties or errors. For example, in a graph describing protein interactions, traditional experimental errors lead to errors in the graph. Another reason is missing data; another example, the Internet graph is determined by examining routing or tracerouting paths, while routing tables and tracerouting path sets only give a subset of edges. This makes the above assumption not valid, that is to say, the graph training samples used for training are not necessarily correct.

Training a graph processing model based on incorrect graph training samples may limit the representation capability of the graph processing model, thereby affecting the accuracy of the graph processing model in practical applications. A typical example is that the performance of graph processing models can degrade significantly on graphs with poor homogeneity (i.e. nodes within the same community tend to be connected to each other). In short, due to the prevalence of missing, meaningless, or even wrong edges in the graph training samples, this leads to a mismatch with the nature of the graph processing model, which affects the accuracy of the graph processing model.

Based on this, the inventors found that it is urgent to explore graph training samples suitable for graph processing models. However, it is currently technically challenging to efficiently learn graph training samples suitable for graph processing models. Much literature in network science has demonstrated that graph generation may be subject to certain principle-based constraints, such as configuration models. Considering these principles, the learned graph can be fundamentally driven to maintain a regular global structure and be more robust to noise in real observations. However, most of the above methods parameterize each edge of the graph without considering the global structure and the underlying generation mechanism of the graph. Therefore, the learned graph is less tolerant to noise and sparsity. In addition, learning a graph from one information source inevitably leads to bias and uncertainty, and it is reasonable to assume that if an edge exists in multiple measurements, the confidence that the edge exists will be greater.

To sum up, a new graph processing model is proposed in the embodiment of the present invention, which is called a graph structure estimation model. Referring to FIG. 2, it is a schematic structural diagram of a graph structure estimation model provided by an embodiment of the present invention. The graph processing model 200 shown in FIG. 2 may also be called a graph structure estimation neural network (GEN). The processing model 200 includes a graph prediction model 201 and a graph estimator 202. The graph prediction model 201 is used to predict the category to which each node in any graph input into the graph prediction model belongs. The graph prediction model may be constructed based on a graph neural network. For example, the graph prediction model is a model constructed based on the graph convolutional network GCN in the graph neural network; the graph estimator 202 is configured to perform estimation according to the observation information input to the graph estimator to obtain an estimated graph. The input to the graph estimator 202 is obtained during the prediction process for any graph according to the graph prediction model.

Based on the new graph structure estimation model shown in FIG. 2 , an embodiment of the present invention provides a model processing solution, and the model processing solution is used to train the graph structure estimation model 200 shown in FIG. 2 . Specifically, the graph prediction model 201 in the graph structure estimation model 200 is called to perform prediction processing on the initial graph (the initial graph may be referred to as a graph training sample) to obtain the observation information that the graph prediction model 201 observes the initial graph; then call The graph estimator 202 in the graph structure estimation model 200 estimates an estimated graph according to the observation information and the label information corresponding to the initial graph; further, the estimated graph is input into the graph prediction model 201 for prediction to obtain prediction information, and then based on the The prediction information and label information optimize the graph prediction model 201 . If the end training instruction is detected, the optimized graph prediction model and the graph estimator are combined into an optimized graph structure estimation model.

Subsequently, if it is detected that the graph to be identified is input into the optimized graph structure estimation model, the graph prediction model 201 in the graph structure estimation model is called to perform prediction processing on the to-be-identified graph to obtain observation information; further, the graph structure estimation model is called. The graph estimator 202 in the model performs estimation processing based on the observation information to obtain an estimated graph; then calls the graph prediction model to perform prediction processing on the estimated graph, and outputs the processing result.

It can be seen that in the process of training a new graph structure estimation model using the model processing scheme in the embodiment of the present invention, the optimization of the graph prediction model is not only based on the initial graph and the label information corresponding to the initial graph, but also The graph structure estimation model is optimized based on the estimation graph. The estimated graph is obtained by estimating the observation information obtained by the graph estimator predicting the initial graph based on the graph prediction model. In other words, the estimated graph is obtained by observing the initial graph from the perspective of the graph prediction model, that is, Compared with the initial graph, the estimated graph can better match the properties of the graph prediction model, which is also more in line with the properties of the graph structure estimation model. Therefore, optimizing the training of the graph prediction model based on the estimated graph can improve the accuracy of the graph prediction model, thereby improving the accuracy of the graph structure estimation model.

Based on the above-mentioned new graph structure estimation model and model processing scheme, an embodiment of the present invention provides a model processing method. Referring to FIG. 3 , which is a schematic flowchart of a model processing method provided by an embodiment of the present invention, the model processing method shown in FIG. 3 may be executed by a model processing device, and specifically may be executed by a processor of the model processing device. The model processing device may refer to a terminal or a server, wherein the terminal may be a smart phone, a tablet computer, a notebook computer, a desktop computer, a smart speaker, a smart watch, etc., but is not limited to this; the server may be an independent physical server, It can also be a server cluster or distributed system composed of multiple physical servers, and can also provide cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, and security services. , CDN, and cloud servers for basic cloud computing services such as big data and artificial intelligence platforms. The model processing method shown in FIG. 3 may include the following steps:

Step S301 , acquiring an initial image and label information corresponding to the initial image.

其中

表示初始图包括的节点的集合，假设初始图中包括N个节点，则

ε表示初始图中边的集合，X表示初始图的节点特征矩阵，X可以表示为：

x_i是指节点v_i的特征向量，i大于等于1小于等于N。In one embodiment, the initial graph may be any graph, and the initial graph may include multiple nodes. Optionally, it is assumed that the initial graph can be represented as

in

Represents the set of nodes included in the initial graph. Assuming that the initial graph includes N nodes, then

ε represents the set of edges in the initial graph, X represents the node feature matrix of the initial graph, and X can be expressed as:

x _i refers to the feature vector of node v _i , i is greater than or equal to 1 and less than or equal to N.

v₁对应的标签信息可以表示为y₁，v₂对应的标签信息可以表示为y₂，以此类推，初始图对应的标签信息可以表示为

Optionally, the label information corresponding to the initial graph is used to indicate the category to which the target node in the initial graph belongs, and the target node may refer to any one or more of multiple nodes included in the initial graph. For example, the target node in the initial graph is represented as

The label information corresponding to v ₁ can be expressed as y ₁ , the label information corresponding to v ₂ can be expressed as y ₂ , and so on, the label information corresponding to the initial graph can be expressed as

As can be seen from the foregoing, the edges in the initial graph are used to describe the relationship between nodes. In addition, the relationship between the nodes in the initial graph can also be represented by the adjacency matrix corresponding to the initial graph. Each row and column in the adjacency matrix is used to represent the vertices in the initial graph, and the matrix stored at the position of v _i row v _j column The element indicates whether there is an edge between node v _i and node v _j , where j is greater than or equal to 1 and less than or equal to N. In this way, the initial graph can be constructed based on the adjacency matrix. Therefore, in the field of graph processing, any graph can also be represented by the adjacency matrix corresponding to the any graph.

For example, suppose that if there is an edge between two nodes, the matrix element at the intersection of the two nodes is 1; if there is no edge between the two nodes, the matrix element at the intersection of the two nodes is 0. Referring to FIG. 4a, which is a schematic diagram of an initial graph provided by an embodiment of the present invention, assuming that the initial graph is an undirected graph, an adjacency matrix corresponding to the initial graph may be shown as 401 in FIG. 4b. It can be seen from Figure 4a that there is an edge between node v0 and node v1. Therefore, in the adjacency matrix shown in Figure 4b, the matrix element 402 at the intersection of node v0 and node v1 is 1; there is no node v1 and node v5. edge, therefore, in the adjacency matrix shown in Figure 4b, the matrix element 403 at the intersection of node v1 and node v5 is 0.

Step S302 , calling the graph prediction model included in the graph structure estimation model to perform prediction processing on the initial graph to obtain observation information corresponding to the initial graph, where the observation information includes prediction information corresponding to the initial graph.

As can be seen from the foregoing, the graph structure estimation model can be composed of a graph prediction model and a graph estimator, wherein the graph prediction model is used to perform prediction processing on the initial graph input to the graph prediction model, and obtain the prediction information corresponding to the initial graph. It indicates the category of each node in the initial graph; in addition, the graph prediction model will generate a neighbor graph set corresponding to the initial graph in the process of predicting the initial graph. The neighbor graph set and the prediction information form the graph prediction model. Observational information for observations. The graph estimator is used to estimate the observation information of the initial graph according to the graph prediction model, and obtain the estimated graph corresponding to any graph.

Optionally, the graph prediction model may be constructed based on a graph neural network, for example, constructed based on a graph convolutional neural network GCN, or constructed based on a graph neural network GNN. In the embodiment of the present invention, a graph prediction model is preferably constructed based on the graph convolutional neural network GCN,

In one embodiment, the graph prediction model may include multiple convolutional layers, each convolutional layer is used to perform convolutional processing on the data input to the convolutional layer, and the output of the previous convolutional layer is used as the next convolutional layer layer input. In the embodiment of the present invention, the graph prediction model includes two convolutional layers as an example to illustrate the working principle of the graph prediction model. In practical applications, the number of convolutional layers of the graph prediction model can be set according to actual requirements.

Specifically, the graph prediction model includes a first convolutional layer and a second convolutional layer, and the graph prediction model included in the graph structure estimation model is used to perform prediction processing on the initial graph to obtain observation information corresponding to the initial graph, including:

Obtain the node feature matrix of the initial graph, and input the node feature matrix into the first convolution layer to perform a convolution operation based on the first weight parameter corresponding to the first convolution layer to obtain a first node Representation matrix; input the first node representation matrix to the second convolution layer for convolution to perform convolution operation based on the second weight parameter corresponding to the second convolution layer to obtain the second node representation matrix, and normalizing the second node representation matrix to obtain the prediction information corresponding to the initial graph; constructing a first neighbor graph based on the first node representation matrix, and constructing a second neighbor graph based on the second node representation matrix a neighbor graph, and the first neighbor graph and the second neighbor graph form the neighbor graph set.

The following is a detailed introduction: the graph prediction model of the embodiment of the present invention is constructed based on the GCN network, and the GCN follows the neighborhood aggregation strategy, and iteratively updates the node representation matrix by aggregating the node representations of the neighbors. Formally, the kth convolution of the GCN The layer aggregation rule can be shown in formula (1):

表示初始图对应的归一化的邻接矩阵，

表示初始图对应的度矩阵，度矩阵对角上的矩阵元素是邻接矩阵所在行求和，具体地可以通过如下公式(2)表示：In formula (1),

represents the normalized adjacency matrix corresponding to the initial graph,

Represents the degree matrix corresponding to the initial graph. The matrix elements on the diagonal of the degree matrix are the sum of the rows of the adjacency matrix. Specifically, it can be expressed by the following formula (2):

In formula (1), W ^(k) represents the weight matrix of the kth convolutional layer, the weight matrix of each convolutional layer constitutes the model parameters of the graph prediction model, and the value of k is greater than or equal to 1 and less than or equal to the graph prediction The number of convolutional layers included in the model. In the embodiment of the present invention, it is assumed that the graph prediction model includes two convolutional layers, so the value of k is greater than or equal to 1 and less than or equal to 2. In the graph prediction model, each convolutional layer corresponds to a weight matrix, and the weight matrix corresponding to each convolutional layer constitutes the model parameters of the graph prediction model. Optionally, assuming that the weight matrix corresponding to the first convolutional layer is represented as W ⁽¹⁾ and the weight matrix corresponding to the second convolutional layer is represented as W ⁽²⁾ , then the model parameters of the graph prediction model can be represented as: Θ=(W ⁽¹⁾ ,W ⁽²⁾ ).

In formula (1), σ represents the activation function, H ^(k-1) represents the node representation matrix corresponding to the k-1th convolutional layer, and H ^(k) represents the node representation matrix corresponding to the kth convolutional layer. As a special case, the node feature matrix X corresponding to the initial graph may also be represented in the form of a node representation matrix, for example, H ⁽⁰⁾ =X. The prediction information corresponding to the initial graph is obtained by normalizing the node representation matrix output by the last convolution layer. Assuming that the graph prediction model has only one convolution layer, the prediction information corresponding to the initial graph can be expressed as Z=H ^{( 1)} .

由前述可知，H⁽⁰⁾＝X表示初始图对应的节点特征矩阵。基于H⁽⁰⁾构建的邻居图(kNN)的邻接矩阵表示为O⁽⁰⁾，基于第一节点表示矩阵构建的邻居图的邻接矩阵表示为O⁽¹⁾，以此类推，基于上述节点表示集合构建的邻居图集合表示为

After the node representation matrix corresponding to the first convolutional layer and the node representation matrix corresponding to the second convolutional layer are obtained based on the above description, further, a neighbor graph set is constructed based on each node representation matrix. Specifically, it is assumed that the node representation matrix corresponding to each convolutional layer forms a node representation set with the node feature matrix of the initial graph

It can be seen from the foregoing that H ⁽⁰⁾ =X represents the node feature matrix corresponding to the initial graph. The adjacency matrix of the neighbor graph (kNN ^{) constructed based on H (0)} is represented as O ⁽⁰⁾ , the adjacency matrix of the neighbor graph constructed based on the first node representation matrix is represented as O ⁽¹⁾ , and so on, based on the above node representation The set of neighbor graphs constructed by the set is represented as

It should be understood that the initial graph is also an important external observation used by the graph prediction model to observe the initial graph. Therefore, in the embodiment of the present invention, the initial graph and the above-mentioned neighbor graph set are used as the observation graph set for observing the initial graph. Further, the observation graph set corresponding to the initial graph and the prediction information corresponding to the initial graph are input into the graph estimator as observation information.

In one embodiment, the graph prediction model included in the graph structure estimation model in step S302 may be a model that has been pre-trained and has reached convergence. In this embodiment of the present invention, after the initial graph is obtained, the graph prediction model does not need to be trained. Step S302 can be directly executed. Alternatively, in order to improve the degree of adaptation between the graph prediction model and the initial graph, even if the graph prediction model has reached convergence before starting step S302, the embodiment of the present invention may further analyze the graph prediction model based on the initial graph and the label information corresponding to the initial graph. optimize.

In other embodiments, if the graph prediction model is not trained to converge before step S302 is performed, the model processing device in this embodiment of the present invention needs to perform training and optimization on the graph prediction model based on the initial graph and label information corresponding to the initial graph.

In one embodiment, if the embodiment of the present invention needs to optimize the graph prediction model based on the initial graph and the label information corresponding to the initial graph, after the graph prediction model performs prediction processing on the initial graph for the first time to obtain the neighbor graph set , may also include: obtaining the prediction information corresponding to the target node from the prediction information corresponding to the initial graph, and determining the difference information between the prediction information corresponding to the target node and the label information; information to construct a loss function corresponding to the graph prediction model;

Update the first weight parameter and the second weight parameter according to the direction of reducing the value of the loss function; update the prediction information and the corresponding prediction information of the initial graph based on the updated first weight parameter and the updated second weight parameter the set of neighbor graphs.

则图预测模型对应的损失函数可以表示为如下公式(3)所示：The loss function corresponding to the graph prediction model can be a cross-entropy function. If the initial graph is represented by the adjacency matrix A corresponding to the initial graph, the node feature matrix corresponding to the initial graph is X, and the label information corresponding to the initial graph is identified as

Then the loss function corresponding to the graph prediction model can be expressed as the following formula (3):

是图预测模型学得的映射函数，

是节点v_i对应的预测信息，

用于衡量任意一个节点的预测信息和该节点的标签信息之间的差异。In formula (3),

is the mapping function learned by the graph prediction model,

is the prediction information corresponding to node v _i ,

It is used to measure the difference between the prediction information of any node and the label information of the node.

To sum up, if the graph prediction model does not need to be optimized based on the initial graph and the label information corresponding to the initial graph in the embodiment of the present invention, step S302 is obtained through a prediction process of the graph prediction model. That is to say, the initial graph is input into the graph prediction model for processing, and the observation information corresponding to the initial graph can be output; if the model processing device in the embodiment of the present invention needs to perform the graph prediction model based on the initial graph and the label information corresponding to the initial graph optimization, then step S302 is obtained by performing multiple prediction processes through the graph prediction model, and the model parameters of the graph prediction model used in each prediction process are optimized based on the prediction information obtained in the previous prediction process and the label information corresponding to the initial graph, In each prediction process, the prediction information corresponding to the initial graph and the set of neighbor graphs are updated along with it; when the graph prediction model reaches convergence, the prediction information and the set of neighbor graphs corresponding to the initial graph of the last prediction process are written into the observation information.

Step S303 , call the graph estimator included in the graph structure estimation model to perform estimation processing based on the label information and the observation information to obtain an estimated graph, and call the graph prediction model to perform prediction processing on the estimated graph to obtain prediction information corresponding to the estimated graph.

After obtaining the observation information corresponding to the initial graph through step S302, the question we need to solve is: based on these observation information, what is the estimated graph that matches the graph prediction model? These observations reveal estimated graphs that match the graph prediction model from different perspectives, but they may be unreliable or incomplete, and there is no prior knowledge to determine the accuracy of any kind of observation. In this case, it is not easy to answer the above question directly, but it is relatively easy to answer the opposite question. Assuming that an estimated graph corresponding to the initial graph matching the graph prediction model has been generated, the model processing device can calculate the probability of mapping the estimated graph to the above-mentioned observation information. If you master this, you can perform inversion based on Bayesian inference and calculate the posterior distribution of the graph structure, so as to achieve the purpose of obtaining an estimated graph that matches the graph prediction model.

That is to say, after obtaining the observation information corresponding to the initial graph in the embodiment of the present invention, the graph estimator first estimates a plurality of candidate graphs corresponding to the initial graph; , then the probability of the existence of the observation information; then, when each candidate image is used as an estimated image, the probability of the existence of the observation information and the corresponding generation probability of each candidate image are estimated to obtain an estimated image that matches the image prediction model.

Specifically, the graph estimator may include a structural sub-model and an observation sub-model. Multiple candidate graphs corresponding to the initial graph are executed by calling the structural sub-model. When any candidate graph is used as an estimated graph matched by the graph prediction model, the probability of existence of observation information is performed by calling the observation sub-model; specifically, the graph estimator included in the call graph structure estimation model performs estimation processing based on the label information and the observation information to obtain an estimation graph, including:

Invoke the structural sub-model to generate N candidate graphs based on the label information and the prediction information in the observation information, and based on the first parameter of the structural sub-model and each candidate graph in the N candidate graphs The corresponding adjacency matrix determines the generation probability corresponding to the corresponding candidate graph; calling the observation sub-model to calculate the corresponding candidate graph based on the second parameter of the observation sub-model, the observation information, and the adjacency matrix corresponding to each candidate graph The existence probability of the corresponding observation information; wherein, the existence probability of the observation information corresponding to the candidate image m is used to indicate the existence probability of the observation information when the candidate image m is used as the estimated image, and m is greater than or equal to 1 and less than equal to N; perform graph estimation based on the generation probability corresponding to each candidate graph and the existence probability of observation information corresponding to each candidate graph to obtain an estimated adjacency matrix, and generate the estimated graph according to the estimated adjacency matrix.

In one embodiment, the graph estimator may be trained when the graph structure estimation model is constructed, and there is no need to train the graph estimator in this embodiment of the present invention; For an estimated graph that matches the model better, the graph estimator can also be optimized during the estimation process based on the label information and observation information. This part of the content will be described in detail in the following embodiments.

Step S304 , optimize the graph prediction model based on the prediction information and label information corresponding to the estimated graph.

After the estimation graph is obtained, the graph prediction model is called to perform prediction processing on the estimation graph, and the prediction information corresponding to the estimation graph is obtained, and then the graph prediction model is optimized based on the prediction information corresponding to the estimation graph and the label information corresponding to the initial graph. It should be understood that the estimated graph is obtained by estimating the observation information of the initial graph based on the graph prediction model. Then, compared with the initial graph, the estimated graph matches the characteristics of the graph prediction model better, and the graph prediction model is optimized based on the estimated graph. , which can improve the accuracy of the graph prediction model.

In one embodiment, optimizing the graph prediction model based on the prediction information and label information corresponding to the estimation graph may include: obtaining the prediction information corresponding to the target node from the prediction information corresponding to the estimation graph; determining the prediction information corresponding to the target node and Difference information between label information; construct a loss function corresponding to the graph prediction model according to the difference information; update the first weight parameter and the second weight parameter of the graph prediction model according to the direction of reducing the value of the loss function, so as to realize the graph prediction model is optimized.

It should be understood that the above steps S301 to S304 only describe the first round of training process for the graph structure estimation model. If after step S304, no end training event is detected, the call graph prediction model is obtained to perform prediction processing on the estimation graph. During the processing, the observation information corresponding to the estimated graph is estimated; the graph estimator is called to perform estimation processing based on the label information and the observation information corresponding to the estimated graph to obtain a new estimated graph, and the optimized graph prediction model is called to predict the new estimated graph processing to obtain the prediction information corresponding to the new estimation graph; the optimized graph prediction model is re-optimized based on the prediction information corresponding to the new estimation graph and the label information corresponding to the optimized graph. The training end event may refer to the above-mentioned training process being executed a preset number of times, or the training end event may also refer to the receipt of an instruction or operation indicating that the training ends.

In the embodiment of the present invention, a new graph processing model is proposed, which is called a graph structure estimation model, and the graph structure estimation model is composed of a graph prediction model and a graph estimator. In the process of optimizing the graph structure estimation model, the graph prediction model in the graph structure estimation model can be invoked to perform prediction processing on the initial graph to obtain observation information corresponding to the initial graph, where the observation information includes the corresponding initial graph. The prediction information of Prediction information; optimize the graph prediction model based on the prediction information corresponding to the estimated graph and the label information corresponding to the initial graph.

It can be seen from the above process that the optimization of the graph prediction model is not only based on the initial graph and the label information corresponding to the initial graph, but also optimizes the graph prediction model based on the estimated graph. The estimated graph is obtained by estimating the observation information obtained by the graph estimator predicting the initial graph based on the graph prediction model. In other words, the estimated graph is obtained by observing the initial graph from the perspective of the graph prediction model, that is to say, the estimated graph better matches the properties of the graph prediction model than the initial graph, which is more in line with the graph structure. Estimate the properties of the model. Therefore, optimizing the training of the graph prediction model based on the estimated graph can improve the accuracy of the graph prediction model, thereby improving the accuracy of the graph structure estimation model.

Based on the above model processing method, an embodiment of the present invention provides another model processing method. Referring to FIG. 5 , it is a schematic flowchart of another model processing method provided by an embodiment of the present invention. The model processing method shown in FIG. 5 can be executed by a model processing device, and specifically, can be executed by a processor of the model processing device. The model processing device may refer to a terminal or a server, wherein the terminal may be a smart phone, a tablet computer, a notebook computer, a desktop computer, a smart speaker, a smart watch, etc., but is not limited to this; the server may be an independent physical server, It can also be a server cluster or distributed system composed of multiple physical servers, and can also provide cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, and security services. , CDN, and cloud servers for basic cloud computing services such as big data and artificial intelligence platforms. The model processing method shown in FIG. 5 may include the following steps:

Step S501 , acquiring an initial image and label information corresponding to the initial image.

Step S502 , calling the graph prediction model included in the graph structure estimation model to perform prediction processing on the initial graph to obtain observation information corresponding to the initial graph, where the observation information includes prediction information corresponding to the initial graph.

In one embodiment, for some feasible implementation manners included in step S501 and step S502, reference may be made to the description of the relevant steps in the embodiment of FIG. 3, and details are not repeated here.

Step S503 , calling the graph estimator included in the graph structure estimation model to perform estimation processing based on the label information and the observation information to obtain an estimation graph.

In one embodiment, as can be seen from the embodiment shown in FIG. 3 , the graph estimator included in the call graph structure estimation model performs estimation processing based on label information and observation information to obtain an estimation graph, including the following steps:

① Invoke the structural sub-model to generate N candidate graphs based on the label information and the prediction information in the observation information, and based on the first parameter of the structural sub-model and each of the N candidate graphs The adjacency matrix corresponding to the candidate image determines the generation probability corresponding to the corresponding candidate image;

② Invoke the observation sub-model to calculate the existence probability of the observation information corresponding to the corresponding candidate graph based on the second parameter of the observation sub-model, the observation information and the adjacency matrix corresponding to each candidate graph; wherein, the candidate graph The existence probability of the observation information corresponding to the graph m is used to indicate the existence probability of the observation information when the candidate graph m is used as the estimated graph, and m is greater than or equal to 1 and less than or equal to N;

③ Perform graph estimation based on the generation probability corresponding to each candidate graph and the existence probability of observation information corresponding to each candidate graph to obtain an estimated adjacency matrix, and generate the estimated graph according to the estimated adjacency matrix.

It can be known from the foregoing description that the graph prediction model in the embodiment of the present invention is constructed based on the GCN network. Considering the local smoothness of the GCN network, the random block model SBM can be used as the structural sub-model, and the random block model can be widely used in the community. Detection, suitable for modeling graphs with relatively strong community structure. The intra-community and inter-community parameter values in the random block module SBM can constrain the homogeneity of the estimated graph.

Optionally, it is assumed that the N candidate pictures include a first candidate picture, and the first candidate picture may be any one of the N candidate pictures. The following takes the first candidate picture as an example to introduce the specific implementation of the above step ①. The generation probability corresponding to the first candidate image is determined based on the first parameter of the structural sub-model and the adjacency matrix corresponding to the first candidate image, and the generation probability corresponding to the first candidate image can be expressed as the following formula (4):

in,

可以表示候选图m的生成概率，在此处假设候选图m是指第一候选图，G是第一候选图对应的邻接矩阵，Z表示观测信息包括的预测值，

表示初始图对应的标签信息；Ω表示结构子模型的第一参数，该第一参数假设节点间边的存在概率仅取决于其社区。例如，社区c_i的节点v_i和社区c_j的节点v_j间边的存在概率表示为

按照上述公式(4)和公式(5)可以得到各个候选图对应的生成概率。In formula (4),

It can represent the generation probability of the candidate map m. Here, it is assumed that the candidate map m refers to the first candidate map, G is the adjacency matrix corresponding to the first candidate map, and Z represents the predicted value included in the observation information,

represents the label information corresponding to the initial graph; Ω represents the first parameter of the structural sub-model, which assumes that the existence probability of an edge between nodes depends only on its community. For example, the existence probability of an edge between node v _{i of community c i and} node v _j of community c _j is expressed as

The generation probability corresponding to each candidate image can be obtained according to the above formula (4) and formula (5).

After obtaining the N candidate graphs and the corresponding generation probability of each candidate graph in the N candidate graphs, the next thing to do is to introduce an observation sub-model to describe how each candidate graph is mapped to the observation information. The first candidate image in the N candidate images is still taken as an example below, and the implementation manner of the foregoing step ② is described in detail. The following introduction assumes that edge observations are independent, uniformly distributed Bernoulli random variables, conditioned on the presence or absence of edges in the candidate graph. Specifically, calling the observation sub-model based on the second parameter of the observation sub-model, the observation information, and the adjacency matrix corresponding to each candidate graph, to calculate the existence probability of the observation information corresponding to the corresponding candidate graph, including the following steps:

S51: Acquire the total number of data included in the observation information, and determine an observation probability parameter according to the second parameter;

It can be seen from the foregoing that the observation information includes the prediction information corresponding to the initial graph, the set of neighbor graphs, and the initial graph. It should be understood that the initial graph includes multiple nodes, and the prediction information corresponding to the initial graph is used to indicate the category to which each node in the initial graph belongs. Therefore, in essence, the prediction information corresponding to the initial graph may include a data indicating the category to which each node belongs. The predicted value of each node; the neighbor graph set includes the target neighbor graph obtained from the node feature matrix corresponding to the initial graph, and multiple neighbor graphs obtained from the node representation matrix corresponding to each convolutional layer of the graph prediction model.

The total amount of data included in the observation information refers to the total amount of the above information. For example, the initial graph includes 5 nodes, the graph prediction model includes 2 convolutional layers, the prediction information includes 5 predicted values, and the neighbor graph The set includes 1 target neighbor graph and 2 neighbor graphs obtained from the node representation matrix. The total number of data included based on this observation information can be equal to: 5 predicted values + 3 neighbor graphs + 1 initial graph = 8.

In one embodiment, the observation probability parameter determined according to the second parameter may include four types, namely, the first type parameter, the second type parameter, the third type parameter, and the fourth type parameter. The first type of parameter refers to the probability that any data in the observation set indicates the existence of an edge between node i and node j when there is an edge between node i and node j; the second type of parameter The parameter refers to the probability that when there is an edge between node i and node j, any data in the observation set indicates that the edge between node i and node j does not exist; the third type of parameter refers to when node i and node j When there is no edge between j, any data in the observation set indicates the probability that the edge between node i and node j does not exist, and the fourth type of parameter refers to when there is no edge between node i and node j When there is an edge, any data in the observation set indicates the probability that an edge exists between the node i and the node j.

In layman's terms, it is assumed that the second parameter of the observation sub-model includes α and β, and each data in the observation information is parameterized by these two parameters. For example, true-positive represents the first type of parameter, and the value of this parameter is α, which means that any data observes the probability that a real edge exists in any candidate graph; false-positive means the third type of parameter, the value of this parameter is β, which means that any data observes any candidate The probability that a real edge does not exist in the graph; true-negative represents the second type parameter, and the value of this parameter is 1-α, which means that any data observes that a real edge does not exist in any candidate graph The probability of ; false-negative represents the fourth type of parameter, and the value of this parameter can be 1-β, which means that any data observes the probability that a real non-existent edge does not exist in any candidate graph.

S52: Acquire a first quantity of data indicating that an edge exists between node i and node j in the observation information, and determine that the observation set indicates that there is no edge between node i and node j according to the first quantity and the total quantity The second quantity of edge data; wherein, node i and node j are any two nodes included in the first candidate graph and i is less than j;

S53: Calculate the edge correlation probability between node i and node j according to the observation probability parameter, the first quantity and the second quantity;

Among them, the edge correlation probability between node i and node j is obtained by multiplying two probabilities, one is that if the edge between node i and node j in the first candidate graph really exists, then the data included in the observation information The probability of the first number of edges appearing between node i and node j; the other is that the edge between node i and node j in the first candidate graph does not really exist, then the data included in the observation information is node i and node j. The probability that the first number of edges appear between.

For example, assuming that the total number of data included in the observation information is M, and the first quantity of data indicating the existence of an edge between node i and node j in the observation information is represented as E _ij , then the observation information indicates that node i and node j The second quantity of data between which no edges exist is ME _ij . The observation probability parameter, the first quantity and the second quantity are input into the calculation formula of the edge correlation probability between nodes for operation, and the edge correlation probability between node i and node j is obtained. Based on this, according to the observation probability parameter, the first The edge correlation probability between node i and node j calculated by a quantity and the second quantity can be expressed as formula (6):

表示如果在第一候选图中节点i和节点j之间的边真实存在，那么观测信息包括的数据中节点i和节点j之间出现第一数量个边的概率；

表示如果在第一候选图中节点i和节点j之间的边真实不存在，那么观测信息包括的数据中节点i和节点j之间出现第一数量个边的概率。In formula (6), G represents the adjacency matrix corresponding to the first candidate graph, G _ij is a matrix element in the adjacency matrix, the value depends on whether there is an edge between node i and node j in the first candidate graph, if The value is 1 if there is an edge between node i and node j, and the value is 0 if there is no edge between node i and node j. In formula (6),

Indicates that if the edge between node i and node j actually exists in the first candidate graph, then the probability of the first number of edges appearing between node i and node j in the data included in the observation information;

Indicates that if the edge between node i and node j does not really exist in the first candidate graph, then the probability that the first number of edges appear between node i and node j in the data included in the observation information.

S54: Multiply the edge correlation probabilities between every two nodes in the first candidate graph to obtain the existence probability of the observation information corresponding to the first candidate graph.

According to the above method, the edge correlation probability between every two nodes in the first candidate graph can be calculated. Further, the first candidate graph can be obtained by multiplying the edge correlation probability between every two nodes in the first candidate graph. The probability of existence of observation information corresponding to the graph. It can be seen from the foregoing that the existence probability of observation information corresponding to the first candidate image is used to represent the probability of existence of observation information when the first candidate image is used as an estimated image.

Optionally, multiply the edge correlation probability between every two nodes in the first candidate graph to obtain the existence probability of the observation information corresponding to the first candidate graph, which can be expressed by the following formula (7):

In one embodiment, the existence probability of the observation information corresponding to each candidate graph in the multiple candidate graphs can be obtained through steps S51 to S54. The existence probability of the observation information corresponding to the candidate graph is subjected to graph estimation processing to obtain an estimated adjacency matrix, and an estimated graph is generated according to the estimated adjacency matrix.

In a specific implementation, it is assumed that the N candidate images include a second candidate image in addition to the first candidate image. Estimation obtains an estimated adjacency matrix, including:

Obtain the probability of the first parameter and the probability of the second parameter; combine the probability of the first parameter, the probability of the second parameter, and the corresponding generation probability of the first candidate map with the first candidate The existence probability of the observation information corresponding to the graph is input into the candidate probability calculation rule for calculation, and the first candidate graph is obtained as the first candidate probability of the estimated graph; the probability of the first parameter, the probability of the second parameter and the The generation probability corresponding to the second candidate picture and the existence probability of the observation information corresponding to the second candidate picture are input into the candidate probability calculation rule for calculation, and the second candidate picture is obtained as the second candidate probability of the estimated picture generating an estimated adjacency matrix based on the first candidate probability, the adjacency matrix corresponding to the first candidate graph, the second candidate probability and the adjacency matrix corresponding to the second candidate graph.

To put it simply, first calculate the first candidate probability of the first candidate image as the estimated image, and the second candidate image of the second candidate image to estimate the second candidate probability of the image, and then based on the first candidate probability and the second candidate probability and the corresponding The adjacency matrix generates an estimated adjacency matrix.

The probability of the first parameter and the probability of the second parameter are respectively determined according to the first parameter and the second parameter, and the probability of the first parameter can be expressed as P(Ω). Since the second parameter includes α and β, Then the probability of the second parameter also includes two, which are respectively expressed as P(α) and P(β). The candidate probability calculation rule can be expressed as the following formula (8):

表示任一候选图对应的生成概率，

表示任一候选图对应的观测信息存在概率。将第一参数的概率、第二参数的概率以及第一候选图对应的生成概率和第一候选图对应的观测信息存在概率带入到公式(8)中边可以得到第一候选图对应的第一候选概率；同理的，将第一参数的概率、第二参数的概率以及第二候选图对应的生成概率和第二候选图对应的观测信息存在概率带入到上述公式(8)中，可以得到第二候选图对应的第二候选概率。In formula (8), G represents the adjacency matrix corresponding to any candidate graph,

represents the generation probability corresponding to any candidate image,

Indicates the existence probability of observation information corresponding to any candidate graph. The probability of the first parameter, the probability of the second parameter, the generation probability corresponding to the first candidate image, and the existence probability of the observation information corresponding to the first candidate image are brought into formula (8) to obtain the first candidate image corresponding to the first candidate image. A candidate probability; similarly, the probability of the first parameter, the probability of the second parameter, the generation probability corresponding to the second candidate map and the existence probability of the observation information corresponding to the second candidate map are brought into the above formula (8), The second candidate probability corresponding to the second candidate map can be obtained.

Optionally, after obtaining the first candidate picture as the first candidate probability of the estimated picture and the second candidate picture as the second candidate probability of the estimated picture through the above formula (8), the first candidate probability and the second candidate probability can be calculated as Generate a probability distribution, denoted as q(G), in which the first candidate probability and the second candidate probability are included. If the N candidate map only includes the first candidate map and the second candidate map, then q(G) The sum of the two candidate probabilities in is equal to 1.

Further, an estimated adjacency matrix is generated based on the first candidate probability, the adjacency matrix corresponding to the first candidate graph, the second candidate probability, and the adjacency matrix corresponding to the second candidate graph.

In the specific implementation, it is assumed that the adjacency matrix corresponding to the first candidate image includes M rows and M columns, then the adjacency matrix corresponding to the first candidate image includes M by M matrix elements. Similarly, the adjacency matrix corresponding to the second candidate image is also Including M rows and M columns, then the adjacency matrix corresponding to the second candidate image also includes M by M matrix elements; the estimated adjacency matrix includes M rows and M columns, and M by M target matrix elements; The candidate probability, the adjacency matrix corresponding to the first candidate graph, the second candidate probability, and the adjacency matrix corresponding to the second candidate graph generate an estimated adjacency matrix, including:

Obtain the first matrix element at the position of the ith row and the jth column in the adjacency matrix corresponding to the first candidate image, and obtain the second element at the position of the ith row and the jth column in the adjacency matrix corresponding to the second candidate image. matrix element; multiply the first matrix element and the first candidate probability to obtain a first operation result, and multiply the second matrix element and the second candidate probability to obtain the first operation result. Two operation results; performing an addition operation on the first operation result and the second operation result, and the operation result is used as the target matrix element at the position of the i-th row and the j-th column in the estimated adjacency matrix.

The above process of calculating the elements of the target matrix can be expressed by formula (9):

In formula (9), G represents the set of adjacency matrices corresponding to the N candidate graphs, G _ij represents the matrix element located at the ith row and the jth column in any adjacency matrix, and Q _ij represents the estimated adjacency matrix located at the ith row The target matrix element in the jth column.

For example, it is assumed that the adjacency matrix corresponding to the first candidate image is shown as 600 in FIG. 6 , the adjacency matrix corresponding to the second candidate image is shown as 601 in FIG. 6 , and the estimated adjacency matrix is shown as 602 in FIG. 6 . The three adjacency matrices are all 5 rows and 5 columns, and include 5 by 5=25 matrix elements. Since the first candidate graph and the second candidate graph are known, then the adjacency matrix of the first candidate graph and the second candidate graph Each matrix element in the matrix of is known, but each target matrix element in the estimated adjacency matrix is unknown, which needs to be obtained from the adjacency matrix of the first candidate graph and the adjacency matrix of the second candidate graph. Specifically, multiplying the matrix element 1 at the position of the first row and the second column in the adjacency matrix 600 with the first candidate probability corresponding to the first candidate image, assuming that the first candidate probability is 0.6, the multiplication result is 0.6; Then multiply the matrix element 0 at the position of the first row and the second column in the adjacency matrix 601 by the second candidate probability corresponding to the second candidate image. Assuming that the second candidate probability is 0.4, the obtained multiplication result is 0; 0+0.6=0.6 as the target matrix element at position 61 in the first row and second column in the estimated adjacency matrix. By analogy, each target matrix element in the estimated adjacency matrix can be obtained.

After the estimated adjacency matrix is obtained through the above steps, an estimated graph can be generated according to the estimated adjacency matrix.

Step S504 , call the graph prediction model to perform prediction processing on the estimated graph, obtain prediction information corresponding to the estimated graph, and optimize the graph prediction model based on the prediction information and label information corresponding to the estimated graph.

In one embodiment, in the process of generating the estimated adjacency matrix in step S503, it is assumed that the first parameter of the structural sub-model and the second parameter of the observation sub-model have been optimized. In practical applications, in order to improve the graph estimator Better matching with the graph prediction model, in the process of generating the estimated adjacency matrix, the first parameter and the second parameter can also be optimized; The adjacency matrix is updated.

In a specific implementation, before generating an estimated adjacency matrix based on the first candidate probability, the adjacency matrix corresponding to the first candidate graph, the second candidate probability, and the adjacency matrix corresponding to the second candidate graph, the method It also includes: performing optimization processing on the first parameter and the second parameter according to the first candidate probability and the second candidate probability; using the optimized first parameter and the optimized second parameter pair The first candidate probability and the second candidate probability are updated respectively. In this way, the estimated adjacency matrix finally generated in step S503 is obtained based on the updated first candidate probability and the updated second candidate probability.

In one embodiment, the performing optimization processing on the first parameter and the second parameter according to the first candidate probability and the second candidate probability includes:

The first candidate probability and the second candidate probability are added together to obtain a joint posterior probability expression of the first parameter and the second parameter; the joint posterior probability is calculated by using a preset inequality Transform the expression; perform a derivation operation on the transformed joint posterior probability based on the first parameter to obtain an optimization equation corresponding to the first parameter, and perform a derivation operation on the changed joint posterior based on the second parameter Perform a derivation operation on the probability to obtain the optimization equation corresponding to the second parameter; solve the optimization equation corresponding to the first parameter to obtain the optimized first parameter, and the optimization corresponding to the second parameter, etc. The second parameter after optimization is obtained by solving the formula.

Wherein, adding the first candidate probability and the second candidate probability to obtain the joint posterior probability expression of the first parameter and the second parameter can be expressed by the following formula (10):

表示N个候选图中候选图m对应的候选概率。In formula (10), G represents the set of adjacency matrices corresponding to each candidate graph in the N candidate graphs,

Indicates the candidate probability corresponding to the candidate map m in the N candidate maps.

Then, the joint posterior probability expression is transformed by using the preset not equal to, for example, Jensen's inequality, that is, transforming the formula (10) to obtain the formula (11):

Further, formula (11) is respectively derived for the first parameter to obtain an optimization equation corresponding to the first parameter, as shown in the following formula (12):

Based on the second optimization parameter, formula (11) is derived, and the optimization equation corresponding to the second parameter is obtained, as shown in the following formulas (13) and (14):

The optimized first parameter can be obtained by solving the formula (12), and the optimized second parameter can be obtained by solving the formula (13) and the formula (14).

For the convenience of calculation, the order of summation of formula (12) can be exchanged, and the following rules are found:

in,

In formula (15), r and s represent two communities, and the interpretation of formula (15) is that the probability of the existence of an edge between community r and community s Ω _rs is the average probability of the existence of an edge between all nodes in these two communities.

Similar calculations are also performed on formula (13) and formula (14), respectively, to obtain formula (16) and formula (17):

The optimized first parameter and the optimized second parameter can be obtained by formulas (15)-(17). Further, the estimated adjacency matrix is updated based on the optimized first parameter and the optimized second parameter. In the specific implementation, the estimated adjacency matrix is updated based on the optimized first parameter and the optimized second parameter, which can be understood as bringing the above formulas (15)-(17) into the formula for determining the estimated adjacency matrix ( 9), rewrite the formula for determining the estimated adjacency matrix, and express the updated estimated adjacency matrix as the following formula (18):

In one embodiment, in the above-mentioned process of optimizing the first parameter and the second parameter, the expression form of the probability distribution q(G) of the existence probability of the observation information is also continuously updated. The right-hand side of the inequality in the above formula (11) is maximized when the equal sign holds, and if the equal sign holds, the expression of q(G) can be expressed as formula (19):

Bringing Equation (4) and Equation (7) into Equation (19), and eliminating the constant in the fraction, the expression of q(G) can be transformed into Equation (20):

Then, formula (20) is rewritten based on formula (18), and finally the expression of q(G) can be obtained as shown in formula (21):

In one embodiment, after the estimated adjacency matrix is updated, an estimated graph can be generated according to the updated estimated adjacency matrix, and further, a graph prediction model is called to perform prediction processing on the estimated graph, to obtain prediction information corresponding to the estimated graph, and based on Estimate the prediction information and label information corresponding to the graph to optimize the graph prediction model.

Optionally, the elements of the target matrix in the estimated adjacency matrix obtained by the above steps are between [0, 1], but the fully connected graph is not only computationally expensive, but also has little meaning for most applications. Therefore, we When generating the estimated graph according to the estimated adjacency matrix, the estimated adjacency matrix may be sparsed first to extract the target adjacency matrix from the estimated adjacency matrix; then, the estimated graph is generated according to the target adjacency matrix.

In a specific implementation, performing sparse processing on the estimated adjacency matrix and extracting a target adjacency matrix from the estimated adjacency matrix includes: traversing each target matrix element in the estimated adjacency matrix, and converting the estimated adjacency matrix The matrix elements less than or equal to the threshold are replaced with zeros to obtain the target adjacency matrix.

For example, assuming that the threshold is set to ε, the extraction of the target adjacency matrix from the estimated adjacency matrix can be expressed by the following formula (22):

Step S505 , if the end training event is not detected, obtain the observation information corresponding to the estimated graph in the process of calling the graph prediction model to predict the estimated graph.

Step S506 , call the graph estimator to perform estimation processing based on the label information and the observation information corresponding to the estimation graph to obtain a new estimation graph, and call the optimized graph prediction model to perform prediction processing on the new estimation graph to obtain a new estimation graph corresponding to forecast information.

Step S507: Update the optimized graph prediction model based on the prediction information and label information corresponding to the new estimated graph.

For some feasible implementation manners included in steps S505 to S507 in an embodiment, reference may be made to the introduction of the relevant steps in the embodiment of FIG. 3 , and details are not repeated here.

In one embodiment, the training of the graph structure estimation model is stopped if an end training event is detected. At this time, if the model processing device acquires a graph to be processed, the graph prediction model in the optimized graph structure estimation model can be invoked to perform prediction processing on the graph to be processed, to obtain target observation information corresponding to the graph to be processed; Then call the graph estimator in the graph structure estimation model to perform estimation processing based on the target observation information to obtain a target estimation graph; call the graph pre-stored model to process the target estimation graph to obtain the prediction corresponding to the target estimation graph As a result, the prediction result is used to indicate the category to which each node in the to-be-processed graph belongs.

The graph structure estimation model trained by the embodiment of the present invention can be applied to any graph structure-based application, such as friend recommendation and advertisement recommendation.

In the embodiment of the present invention, a graph structure estimation model is proposed, which is composed of a graph prediction model and a graph estimator. In the process of optimizing the graph structure estimation model, the graph prediction model in the graph structure estimation model can be invoked to perform prediction processing on the initial graph to obtain observation information corresponding to the initial graph, where the observation information includes the corresponding initial graph. The prediction information of Prediction information; optimize the graph prediction model based on the prediction information corresponding to the estimated graph and the label information corresponding to the initial graph.

Further, if the end training event is not detected, obtain the observation information corresponding to the estimated graph obtained in the process of predicting the estimated graph by the call graph prediction model; the call graph estimator estimates based on the label information and the observation information corresponding to the estimated graph. process to obtain a new estimated graph, and call the optimized graph prediction model to perform prediction processing on the new estimated graph to obtain prediction information corresponding to the new estimated graph. Furthermore, the optimized graph prediction model is updated based on the prediction information and label information corresponding to the new estimated graph. Repeat the above steps continuously until the end training event is detected, then stop training.

It can be seen from the above process that the optimization of the graph prediction model is not only based on the initial graph and the label information corresponding to the initial graph, but also optimizes the graph prediction model based on the estimated graph. The estimated graph is obtained by estimating the observation information obtained by the graph estimator predicting the initial graph based on the graph prediction model. In other words, the estimated graph is obtained by observing the initial graph from the perspective of the graph prediction model, that is to say, the estimated graph better matches the properties of the graph prediction model than the initial graph, which is more in line with the graph structure. Estimate the properties of the model. Therefore, optimizing the training of the graph prediction model based on the estimated graph can improve the accuracy of the graph prediction model, thereby improving the accuracy of the graph structure estimation model.

In order to more vividly describe the training process of the graph structure estimation model in the embodiment of the present invention, based on the method embodiments of FIG. 3 and FIG. 5 , an embodiment of the present invention provides a training schematic diagram of a graph structure estimation model, as shown in FIG. 7 . , and a training algorithm flow as shown in Table 1. The training algorithm shown in Table 1 is applied to the graph structure estimation model shown in FIG. 7 to complete the training of the graph structure estimation model.

According to the training algorithm shown in Table 1, the training process of the graph structure estimation model in the embodiment of the present invention is summarized, which can be roughly summarized as: the node feature matrix (feature matrix) X, the adjacency matrix (adjacency matrix) A and the label information of the initial graph (labels), each neighbor graph (k in kNN), tolerance (tolerance) λ, threshold (threshold) ε, iterations threshold (iterations) τ as input, input into the graph structure estimation model; if the current training round If i is less than or equal to the iteration threshold τ, first update the weight parameter Θ of each convolutional layer of the graph prediction model until the graph prediction model converges; then predict the initial graph based on the converged graph prediction model, and obtain the corresponding Observation information; then update the first parameter Ω of the structural sub-model in the graph estimator and the second parameters α and β of the observation sub-model through steps 5, 6, and 7, and according to the updated first parameter and the updated second parameter Parameter calculation obtains the estimated adjacency moment Q; Further, the estimated adjacency matrix Q is carried out sparse processing again, obtains the target adjacency matrix S ⁽ⁱ⁾ ; According to the target adjacency matrix S ^(i), generate the estimated graph. The above training process is repeated until the current training round i is greater than the iteration number threshold τ, then the training of the graph structure estimation model is ended.

Table 1

In FIG. 7 , the graph structure estimation model 700 includes a graph prediction model 701 and a graph estimator 702 , the graph prediction model may include 1 convolutional layers, and the graph estimator includes a structure sub-model 7021 and an observation sub-model 7022 . In the embodiment of the present invention, the adjacency matrix A corresponding to the initial graph is used to represent the initial graph, the node feature matrix S corresponding to the initial graph is input into the graph prediction model, and each convolutional layer pair in the l convolutional layers included in the graph prediction model is paired The initial graph is subjected to convolution processing, the input of each convolution layer is the input of the previous convolution layer, and each convolution layer obtains the node representation matrix of the layer after the convolution processing, as shown in Figure 7, the first The node representation matrix obtained after the convolution process of one convolution layer is denoted as H ⁽¹⁾ , the node representation matrix obtained by the convolution process of the second convolution layer is denoted as H ⁽²⁾ , and so on, the lth The node representation matrix obtained after the convolution processing of each convolutional layer is performed is represented as H ^(l) ; from the foregoing, it can be seen that the node representation corresponding to the node feature matrix corresponding to the initial graph can be represented as H ⁽⁰⁾ .

Further, a neighbor graph is generated according to the node representation matrix corresponding to each convolutional layer and the adjacency matrix corresponding to the neighbor graph is obtained, as shown in FIG. 7 , according to the node representation matrix H ^{(1 )} The neighbor graph obtained is 703, the adjacency matrix corresponding to the neighbor graph 703 is represented as O ⁽¹⁾ , and the corresponding neighbor graph obtained according to the node representation H ⁽²⁾ matrix corresponding to the second convolutional layer is 704, and the neighbor graph 704 The corresponding adjacency matrix is denoted as O ⁽²⁾ , the neighbor graph constructed according to the node representation matrix H ^(l) corresponding to the lth convolutional layer is denoted as 705, and the adjacency matrix corresponding to the neighbor graph 705 is denoted as O ^(l) . The target neighbor graph constructed according to the node feature matrix S corresponding to the initial graph is 706 , and the adjacency matrix corresponding to the target neighbor graph 706 is represented as O ⁽⁰⁾ . The neighbor graph set and the initial graph are composed of the observation graph set obtained by observing the initial graph.

接着，模型处理设备将最后一个卷积层也就是第i个卷积层的输出进行归一化处理可以得到初始图对应的预测信息，假设初始图对应的预测信息表示为Z。将预测信息Z和观测图集合组成一条观测信息，将观测信息和初始图对应的标签信息输入到图估计器702中，图估计器702中的结构子模型7021基于标签信息生成多个候选图并得到每个候选图的生成概率，观测子模型7022确定每个候选图对应的观测信息存在概率，以及根据每个候选图对应的观测信息存在概率和每个候选图的生成概率得到估计邻接矩阵Q，最后根据估计邻接矩阵Q生成估计图，并将估计图输入至图预测模型701中，继续下一次训练。Further, the initial graph A and each neighbor graph are formed into an observation graph set, and the optional observation graph set can be expressed as:

Next, the model processing device normalizes the output of the last convolutional layer, that is, the ith convolutional layer, to obtain the prediction information corresponding to the initial image, assuming that the prediction information corresponding to the initial image is represented as Z. The prediction information Z and the set of observation graphs are formed into a piece of observation information, and the label information corresponding to the observation information and the initial graph is input into the graph estimator 702, and the structure sub-model 7021 in the graph estimator 702 generates a plurality of candidate graphs based on the label information. Obtain the generation probability of each candidate image, the observation sub-model 7022 determines the existence probability of the observation information corresponding to each candidate image, and obtains the estimated adjacency matrix Q according to the existence probability of the observation information corresponding to each candidate image and the generation probability of each candidate image , and finally generate an estimated graph according to the estimated adjacency matrix Q, and input the estimated graph into the graph prediction model 701 to continue the next training.

In addition, in order to verify the advantages of the graph structure estimation model in the embodiment of the present invention in practical applications, the graph structure estimation model described in the embodiment of the present invention and the graph processing model constructed based on GNN in the prior art are used to compare the graph node The classification performance is compared.

In the specific implementation, the data used for performance comparison are shown in Table 2, from 6 data sets:

Table 2

In Table 2, Cora, Citeseer and Pubmed are the benchmark reference network datasets. In these networks, nodes represent papers and edges represent citation relationships. Node features are bag-of-words representations of papers, while labels are academic domains. Chameleon and Squirrel are topic-specific page-page networks in Wikipedia. In these datasets, nodes are web pages and edges represent hyperlinks. Node features are informational nouns in a page, and tags correspond to monthly traffic to the page. The Actor dataset is an actor subgraph of the fim-director-actor-writer network. Each node represents an actor and an edge represents a collaboration. Node features are keywords in Wikipedia and tags are actor types.

According to the homogeneity of the above datasets, the above 6 datasets can be divided into homographies (Cora, Citeseer and Pubmed) and heterographs (Chameleon, Squirrel and Actor). For the challenging datasets Chameleon, Squirrel, and Actor, the supervision is set to a typical semi-supervised train/validation/test split in this experiment.

In the testing process, the graph structure processing model (GEN) of the embodiment of the present invention is compared with three types of representative GNNs, including three spectrum-based graph processing models (such as SGC, GCN, and ChebNet), three spatial-based Graph processing models (such as GAT, APPNP and GraphSAGE) and three graph processing models based on graph structure learning (such as LDS, Pro-GNN and Geom-GCN). In the embodiment of the present invention, for the convenience of description, SGC, GAT, and LDS are selected for comparison with the GEN that is in progress in the embodiment of the present invention.

In the specific test comparison process, the graph structure estimation model proposed in the embodiment of the present invention is implemented based on the deep learning library PyTorch. All experimental comparisons were performed on a Linux server with a Graphics Processing Unit (GPU) and a Central Processing Unit (CPU).

In the graph structure processing model in the embodiment of the present invention, the graph prediction model is based on GCN, and the Adam optimizer is used to train it for 200 rounds. The initial learning rate is 0.01 and the weight decay is 5e-4. Set ReLU as the activation function of the graph prediction model and apply a dropout of 0.5 to further prevent overfitting. For the web search controls for hyperparameters, choose the embedding dimension d from {8, 16, 32, 64, 128,}, adjust the k of kNN from 3 to 15, the tolerance λ is searched in {0.1, 0.01, 0.001}, and Adjust the threshold ε in {0.1, 0.2, ..., 0.9}. The iteration threshold τ is fixed at 50, and then the model with the highest accuracy on the validation set is selected for testing.

During the experiment, SGC, GCN, GAT, APPNP, and GraphSAGE implemented by PyTorch Geometric were used. For the remaining benchmark methods ChebNet, LDS, Pro-GNN and Geom-GCN, their corresponding source codes are used. A hyperparameter search is performed on all models on the validation dataset. For the sake of fairness, the graph structure estimation model proposed in the embodiment of the present invention and other graph processing models have the same search space size for common hyperparameters, including embedding dimension, initial learning rate, weight decay, and dropout rate.

The performance comparison of the GEN model and other graph processing models used for comparison in terms of node classification performance is shown in Table 3 below: Table 3 only shows the classification performance comparison of GEN, SGC, GAT and LDS on the data set. The classification performance of other unshown models GCN, CheNet, APPNP, GraphSAGE, Pro-GNN and Geom-GCN on the three datasets is also worse than that of GEN; for the same reason, in other datasets except the above three datasets Above, the classification performance of each contrasted graph processing model is also worse than that of GEN. For the convenience of description, the embodiments of the present invention are not listed one by one in the form of a table.

table 3

According to the comparison results, the GEN model consistently outperforms the other models on the 3 datasets, and for the other 3 data sets, although not shown in the table, the GEN model also outperforms the other models. Especially with reduced labels and reduced homogeneity, this shows that the GEN model of embodiments of the present invention can improve node classification performance in a robust manner. The performance of GNNs degrades rapidly as labels and homogeneity decrease, while the performance improvement of GEN models is more pronounced. These phenomena are in line with the expectations of the embodiments of the present invention, that is, noisy or sparse graph structures prevent the GNN from gathering effective information, and the estimation graph of the embodiments of the present invention can alleviate this problem. The overwhelming dominance of GEN over other models means that GEN is able to estimate suitable graph structures. Compared with other models, the performance improvement of the GEN model in the embodiment of the present invention shows that explicitly limiting the community structure and making full use of multi-faceted information helps to learn better graph structures and more reliable GCN parameters.

In Table 2, 20, 5, and 10 labels were set for each class during the experiment, respectively. The mean and standard deviation of 10 random independent trials are shown in Figure 2.

In order to further understand the improvement in performance of the GEN model compared to other graph processing models based on the GNN network, the embodiment of the present invention analyzes the change of the prediction confidence. Specifically, for each training and test set node vi in the Cora and Chameleon datasets _{, the value corresponding to the true class yi of} that node is selected from the final prediction information of the GCN and GEN models and plotted as The box plot shown in Figure 8a.

In the box plot shown in Figure 8a, the box represents 25-75%; the median is represented by a bold dashed line, as shown at 800 in Figure 8a; the solid black circle represents the mean, as shown at 801 in Figure 8a. The whiskers extend to the minimum and maximum data points that are not outliers. For a more intuitive representation, for each box, the prediction confidence for 50 nodes is shown with a dashed grey solid circle, as shown at 802 in Figure 8a. From the graph in Figure 8a, it can be seen that for Cora or the more challenging Chameleon dataset, the prediction confidence obtained on the estimated graph is much higher than the initial graph. It is speculated that injecting multi-order neighbor similarity into graph structure learning can make the learned graph depict more informative node pairs, thus making the classification distribution more spiky and providing GCN with the ability to correct misclassified nodes.

In order to understand the iterative estimation process of GEN, the embodiment of the present invention provides the change curves of true-positive probability α and false-positive probability β on the Cora and Chameleon data sets, as shown in Figure 8b, 81 indicates on the Cora data set Represents the true-positive probability α and 82 represents the change curve of the false-positive probability β on the Cora dataset, 83 represents the true-positive probability α on the Chameleon dataset and 84 represents the change in the false-positive probability β on the Chameleon dataset curve. In Fig. 8b, the coordinates of the horizontal axis represent the alternative steps of expectation and maximization in the EM algorithm, with dashed lines separating different iterations of GEN. The tolerance λ can be fixed to 0.001 in Figure 8b. It can be seen from Figure 8b that during the iterative process, the true-positive probability α gradually increases, which means that the observation information established by the graph prediction model becomes more and more accurate.

In the embodiment of the present invention, the convergence speed of the GEN model and other graph processing models is further compared. Referring to FIG. 9a, it is a graph of the accuracy rate of the GEN model and other graph processing models provided by the embodiment of the present invention. In Figure 9a, 90A represents the accuracy curve of the LDS model on the Cora dataset, 90B represents the accuracy curve of the LDS model on the Chameleon dataset; 91A represents the accuracy curve of the Pro-GNN model on the Cora dataset, 91B represents The accuracy curve of the Pro-GNN model on the Chameleon dataset; 92A represents the accuracy curve of the GEN model on the Cora dataset, and 92B represents the accuracy curve of the GEN model on the Chameleon dataset. In Figure 9a, the abscissa is the number of iteration rounds, and the ordinate is the accuracy. As can be seen in Figure 9a, GEN has faster convergence speed and better validation set accuracy on both datasets, demonstrating the efficiency and effectiveness of GEN. Moreover, for the Chameleon dataset, the validation set accuracy of LDS and Pro-GNN fluctuates greatly, while GEN steadily improves the accuracy, which again confirms the robustness considering the principle of graph generation and multi-faceted information.

The aforementioned comparison of peers has proven the effectiveness of the GEN model on actual data sets. The following describes the mechanism of the GEN model and the properties of the estimation graph.

In order to better explore the GEN mechanism, in the embodiment of the present invention, an attribute stochastic model SBM is used to study the estimated graph, and this model has been widely used in the benchmark graph clustering method. For better visualization and analysis, in the SBM version in this embodiment of the present invention, there are 5 communities, and each community has 20 nodes. A symmetric probability matrix is randomly initialized to generate edges, with diagonal elements being largest in the corresponding row in most cases, to ensure some degree of homogeneity. The 8-dimensional features of nodes are generated using a multivariate normal distribution, where nodes in different communities share a random covariance matrix, but have different means according to their own communities. On the train/validation/test split, we use 5 nodes per class for training, 5 nodes for validation, and the rest as testing.

In order to visually check the graph structure changes brought about by GEN, the Gephi tool is used in the embodiment of the present invention to visualize the initial graph and the estimated graph at 911 and 913 in Fig. 9b. At the same time, zoom in on the local details of the above graph and select a particular node to highlight the changes in its neighborhood in 912 and 914 in Fig. 9b. As can be seen from 911 in Figure 9b, the initial graph is relatively chaotic, and there are many connections between communities, which can be more clearly reflected by the neighborhood of the selected node. In this case, the classification accuracy of the graph prediction model GCN is only 60%. It can be seen from 913 in Fig. 9b that after applying the GEN model of the embodiment of the present invention, the community structure of the estimation graph is clear. Among them, many erroneous edges are removed and strongly connected relationships are preserved, and the classification accuracy of GEN is improved to 84%.

To quantify the transition of community structure before and after estimation, the probability matrix between communities in the initial graph and the probability matrix between communities in the estimated graph can be calculated and plotted as a heatmap. Referring to Fig. 9c, it is a schematic diagram of a probability matrix heat map improved by the invention. In Fig. 9c, 901 denotes the probability matrix between communities in the initial graph, and 902 denotes the probability matrix between communities in the estimated graph. As can be seen from Figure 9c, the off-diagonal color blocks in 901 are also darker, even deeper than the diagonal blocks, which indicates that the initial graph cannot maintain good homogeneity, and high probability connections between communities may give graphs The optimization of predictive models poses difficulties. However, for 902, the difference between the diagonal elements and the off-diagonal elements is enlarged, wherein the former is significantly larger than the latter, which also explains the reason why the classification performance of the graph processing model GEN in the embodiment of the present invention is improved.

Recall that in the embodiments of Figures 3 and 5, the estimated adjacency matrix Q in the GEN is the posterior probability of the graph structure, where Q _ij represents the confidence that the edge exists. To study the significance of estimating an edge, the relationship between the edge confidence Q _ij and the first quantity of data E _ij in the observation information indicating the existence of an edge between node i and node j can be shown. Assuming that the total number of data included in one observation is 3, then E _ij takes values from 0 to 3. For each possible value of _Eij , the corresponding number of node pairs (one node pair consists of two nodes) is accumulated, and the average edge confidence for these node pairs is calculated in Fig. 9d. In Figure 9d, 010 represents the number of node pairs corresponding to each E _ij , and 011 represents the average edge confidence of each E _ij . It can be seen from Figure 9d that most node pairs appear where _Eij equals 0, which is because the graph is sparse and the vast majority of node pairs are difficult to meet. From the relationship between the first quantity E _ij and the average edge confidence, it can be seen that an edge observed only zero or one time means that Q _ij is low, so a single observation may be due to error. However, there is a relatively sharp transition between E _ij =1 and E _ij =2, suggesting that two or more observations of the same edge lead to a larger Qi _ij , which reflects the presence of the edge in the optimal graph higher confidence.

In order to show the distribution of edge confidence, the edges can be divided into two groups, the edges of the same community and the edges of different communities. The normalized histograms of these edge confidences on the training dataset, validation dataset, and test dataset for training the GEN model are shown in Figure 9e below. In Figure 9e, dashed white filled rectangular boxes are used to represent the edges of the same community, and solid black filled matrix boxes are used to represent edges of different communities. It can be observed from Figure 9e that the edge confidences of the same community are gathered in the last region (greater than 0.9), while the edge confidences between different communities are more biased towards the first region (less than 0.1). This shows that GEN captures useful edge confidence, i.e. the edge confidence between the same communities is higher.

In the above description, it is meant that the GEN model is applied to the static graph, and the GEN model can be applied to the dynamic graph in the future. Intuitively, observations can be constructed on different time slices, so GEN can infer graph results based on a series of historical interactions.

Based on the above-mentioned embodiment of the training method of the graph structure estimation model, the embodiment of the present invention provides a training apparatus for the graph structure estimation model. Referring to FIG. 10 , it is a schematic structural diagram of a training apparatus for a graph structure estimation model provided by an embodiment of the present invention. The training device described in Figure 10 may operate the following units:

The obtaining unit 1001 is configured to obtain an initial graph and label information corresponding to the initial graph; the initial graph includes a plurality of nodes, and the label information is used to indicate the category to which a target node in the initial graph belongs, and the target node is any one or more of the multiple nodes of the initial graph;

A processing unit 1002, configured to call a graph prediction model included in the graph structure estimation model to perform prediction processing on the initial graph, and obtain observation information corresponding to the initial graph;

The processing unit 1002 is further configured to call a graph estimator included in the graph structure estimation model to perform estimation processing based on the label information and the observation information to obtain an estimated graph; and call the graph prediction model to perform an estimation on the estimated graph. performing prediction processing to obtain prediction information corresponding to the estimation graph, where the prediction information corresponding to the estimation graph is used to indicate the category to which each node in the estimation graph belongs;

The processing unit 1002 is further configured to optimize the graph prediction model based on the prediction information corresponding to the estimation graph and the label information.

In one embodiment, the obtaining unit 1001 is further configured to: if the end training event is not detected, obtain the observation corresponding to the estimated graph obtained in the process of invoking the graph prediction model to perform prediction processing on the estimated graph information;

The processing unit 1002 is further configured to call the graph estimator to perform estimation processing based on the label information and the observation information corresponding to the estimated graph to obtain a new estimated graph, and call the optimized graph prediction model to perform an estimation process on the new estimated graph. Prediction processing is performed on the estimation graph of , to obtain the prediction information corresponding to the new estimation graph, and the prediction information corresponding to the new estimation graph is used to indicate the category to which each node in the new estimation graph belongs;

The optimized graph prediction model is updated based on the prediction information corresponding to the new estimated graph and the label information.

In one embodiment, the observation information includes prediction information corresponding to the initial graph and a set of observation graphs corresponding to the initial graph, where the prediction information corresponding to the initial graph is used to indicate the category to which each node in the initial graph belongs, and the The observation graph set includes the initial graph and the neighbor graph set corresponding to the initial graph; the graph prediction model includes a first convolution layer and a second convolution layer, and the processing unit 1002 calls the The graph prediction model included in the graph structure estimation model performs prediction processing on the initial graph, and when the observation information corresponding to the initial graph is obtained, the following steps are performed:

Obtain the node feature matrix of the initial graph, and input the node feature matrix to the first convolutional layer to perform a convolution operation based on the first weight parameter corresponding to the first convolutional layer to obtain the first convolutional layer. A node representation matrix corresponding to one convolutional layer; inputting the node representation matrix corresponding to the first convolutional layer to the second convolutional layer to be based on the second weight corresponding to the second convolutional layer The parameters are subjected to convolution operation to obtain the node representation matrix corresponding to the second convolution layer;

normalizing the node representation matrix corresponding to the second convolutional layer to obtain prediction information corresponding to the initial graph; constructing a first neighbor graph based on the node representation matrix corresponding to the first convolutional layer, and Construct a second neighbor graph based on the node representation matrix corresponding to the second convolutional layer, and construct a target neighbor graph based on the node feature matrix of the initial graph; combine the first neighbor graph, the second neighbor graph and the The target neighbor graph forms the neighbor graph set.

In one embodiment, the graph estimator includes a structure sub-model and an observation sub-model, and the processing unit 1002 performs estimation processing based on the label information and the observation information when invoking the graph estimator included in the graph structure estimation model to obtain the result. When estimating the graph, perform the following steps:

Invoke the structural sub-model to generate N candidate graphs based on the label information and the prediction information corresponding to the initial graph in the observation information corresponding to the initial graph, where N is an integer greater than or equal to 1; and based on the structural sub-model The first parameter of and the adjacency matrix corresponding to each candidate image in the N candidate images determine the generation probability corresponding to the corresponding candidate image;

Calling the observation sub-model to calculate the existence probability of the observation information corresponding to the corresponding candidate graph based on the second parameter of the observation sub-model, the observation information corresponding to the initial graph, and the adjacency matrix corresponding to each candidate graph; wherein, The existence probability of the observation information corresponding to the candidate map m is used to indicate that when the candidate map m is used as the estimated map, the probability of the existence of the observation information, m is greater than or equal to 1 and less than or equal to N; The estimated adjacency matrix is obtained by performing graph estimation on the generation probability of , and the existence probability of observation information corresponding to each candidate graph, and the estimated graph is generated according to the estimated adjacency matrix.

In one embodiment, the N candidate graphs include a first candidate graph, and the processing unit 1002 calls the observation sub-model based on a second parameter of the observation sub-model, observation information corresponding to the initial graph, and For the adjacency matrix corresponding to each candidate graph, when calculating the existence probability of the observation information corresponding to the corresponding candidate graph, the following steps are performed:

Acquiring the total number of data included in the observation information, and determining an observation probability parameter according to the second parameter; acquiring the first quantity of data indicating the existence of an edge between node i and node j in the observation information, and determining the observation probability parameter according to the second parameter; The first quantity and the total quantity determine the second quantity of data indicating that there is no edge between node i and node j in the observation information; wherein, node i and node j are any arbitrary data included in the first candidate graph. Two nodes and i is less than j; calculate the edge correlation probability between the node i and node j according to the observation probability parameter, the first number and the second number; The edge correlation probabilities between the nodes are multiplied to obtain the existence probability of the observation information corresponding to the first candidate graph.

In one embodiment, the observation probability parameter includes a first-type parameter, a second-type parameter, a third-type parameter, and a fourth-type parameter; wherein, the first-type parameter refers to the time between node i and node j When there is an edge, any data in the observation set indicates the probability of the existence of an edge between the node i and node j; the second type of parameter refers to the observation when an edge exists between node i and node j Any data in the set indicates the probability that the edge between node i and node j does not exist; the third type of parameter refers to when there is no edge between node i and node j, any data in the observation set Indicates the probability that the edge between the node i and the node j does not exist, and the fourth parameter refers to when there is no edge between the node i and the node j, any data in the observation set indicates that the node i and the probability that an edge exists between node j.

In one embodiment, the N candidate pictures include a first candidate picture and a second candidate picture, and the processing unit 1002 is based on the generation probability corresponding to each candidate picture and the existence probability of observation information corresponding to each candidate picture When performing graph estimation to obtain an estimated adjacency matrix, perform the following steps:

Obtain the probability of the first parameter and the probability of the second parameter; combine the probability of the first parameter, the probability of the second parameter, and the corresponding generation probability of the first candidate map with the first candidate The existence probability of the observation information corresponding to the graph is input into the candidate probability calculation rule for calculation, and the first candidate graph is obtained as the first candidate probability of the estimated graph;

The probability of the first parameter, the probability of the second parameter, the generation probability corresponding to the second candidate map, and the existence probability of the observation information corresponding to the second candidate map are input into the candidate probability calculation rule for operation to obtain the second candidate graph as the second candidate probability of the estimated graph; based on the first candidate probability, the adjacency matrix corresponding to the first candidate graph, the second candidate probability and the second candidate graph The corresponding adjacency matrix generates an estimated adjacency matrix.

In one embodiment, the adjacency matrix corresponding to any candidate graph includes M rows and M columns, the adjacency matrix corresponding to any candidate graph includes M by M matrix elements, and the estimated adjacency matrix includes M rows and M columns, so The estimated adjacency matrix includes M by M target matrix elements; the processing unit 1002 is based on the first candidate probability, the adjacency matrix corresponding to the first candidate map, the second candidate probability and the second candidate When the adjacency matrix corresponding to the graph generates the estimated adjacency matrix. Perform the following steps:

Obtain the first matrix element at the position of the ith row and the jth column in the adjacency matrix corresponding to the first candidate image, and obtain the second element at the position of the ith row and the jth column in the adjacency matrix corresponding to the second candidate image. matrix element; multiply the first matrix element and the first candidate probability to obtain a first operation result, and multiply the second matrix element and the second candidate probability to obtain the first operation result. Two operation results; performing an addition operation on the first operation result and the second operation result, and the operation result is used as the target matrix element at the position of the i-th row and the j-th column in the estimated adjacency matrix.

In one embodiment, the processing unit 1002 is further configured to:

The first parameter and the second parameter are optimized according to the first candidate probability and the second candidate probability; the adjacency matrix is estimated based on the optimized first parameter and the optimized second parameter pair Update processing is performed.

In an embodiment, when the optimization process is performed on the first parameter and the second parameter according to the first candidate probability and the second candidate probability, the following steps are performed:

The first candidate probability and the second candidate probability are added together to obtain a joint posterior probability expression of the first parameter and the second parameter; the joint posterior probability is calculated by using a preset inequality expression to transform;

Perform a derivation operation on the transformed joint posterior probability based on the first parameter to obtain an optimization equation corresponding to the first parameter, and perform a derivation operation on the changed joint posterior probability based on the second parameter , obtain the optimization equation corresponding to the second parameter; solve the optimization equation corresponding to the first parameter to obtain the optimized first parameter, and solve the optimization equation corresponding to the second parameter to obtain the optimized process after the second parameter.

In one embodiment, when the processing unit 1002 generates the estimated graph according to the estimated adjacency matrix, the following steps are performed:

Perform sparse processing on the estimated adjacency matrix, and extract a target adjacency matrix from the estimated adjacency matrix; and generate the estimated graph according to the target adjacency matrix.

In one embodiment, when performing sparse processing on the estimated adjacency matrix and extracting a target adjacency matrix from the estimated adjacency matrix, the processing unit 1002 performs the following steps: traversing each target in the estimated adjacency matrix Matrix elements, replace the matrix elements less than or equal to the threshold value in the estimated adjacency matrix to zero to obtain the target adjacency matrix.

In one embodiment, the prediction information corresponding to the initial graph includes a predicted value corresponding to each node in the multiple nodes of the initial graph, and the predicted value corresponding to any node is used to indicate the category to which any node belongs, The label information includes a target value used to indicate the category to which the target node belongs; the processing unit 1002 is further configured to:

Obtain the predicted value corresponding to the target node from the prediction information corresponding to the initial graph, and determine the difference information between the predicted value corresponding to the target node and the target value included in the label information; according to the constructing a loss function corresponding to the graph prediction model based on the difference information; updating the first weight parameter and the second weight parameter in the direction of reducing the value of the loss function; based on the updated first weight parameter and the updated second weight parameter The weight parameter updates the prediction information corresponding to the initial graph and the neighbor graph set respectively.

In one embodiment, the obtaining unit 1001 is further configured to: obtain the graph to be processed; the processing unit 1002 is further configured to: call the optimized graph prediction model in the graph structure estimation model to perform the processing on the graph to be processed Perform prediction processing to obtain target observation information corresponding to the to-be-processed graph, where the target observation information includes target prediction information corresponding to the to-be-processed graph; call the graph estimator to perform estimation processing based on the target observation information to obtain a target Estimation graph; invoking the graph prediction model to process the target estimation graph to obtain a prediction result corresponding to the target estimation graph, where the prediction result is used to indicate the category to which each node in the graph to be processed belongs.

According to an embodiment of the present invention, each step involved in the training method of the graph structure estimation model shown in FIG. 3 and FIG. 5 may be performed by each unit in the graph structure estimation model training apparatus shown in FIG. 10 . For example, step S301 shown in FIG. 3 can be performed by the acquisition and receiving unit 1001 in the training device of the graph structure estimation model shown in FIG. 10 , and steps S302 to S304 can be performed by the training device of the graph structure estimation model shown in FIG. 10 . For another example, in the training method of the graph structure estimation model shown in FIG. 5, step S501 can be executed by the acquisition unit 1001 in the training device of the graph structure estimation model shown in FIG. 10, step S502-step S507 It can be performed by the processing unit 1002 in the training device of the graph structure estimation model shown in FIG. 10 .

According to another embodiment of the present invention, each unit in the training apparatus of the graph structure estimation model shown in FIG. 10 may be respectively or all combined into one or several other units to form, or some unit(s) among them. It can also be divided into multiple units with smaller functions, which can realize the same operation without affecting the realization of the technical effects of the embodiments of the present invention. The above-mentioned units are divided based on logical functions. In practical applications, the function of one unit may also be implemented by multiple units, or the functions of multiple units may be implemented by one unit. In other embodiments of the present invention, the training apparatus based on the graph structure estimation model may also include other units. In practical applications, these functions may also be implemented with the assistance of other units, and may be implemented by multiple units in cooperation.

According to another embodiment of the present invention, a general-purpose computing device, such as a computer, may be implemented using processing elements such as a central processing unit (CPU), random access storage medium (RAM), read-only storage medium (ROM), etc., and storage elements. Running a computer program (including program code) capable of performing the steps involved in the corresponding methods as shown in Figures 3 and 5, to construct a training device for a graph structure estimation model as shown in Figure 10, and to implement the present invention The training method of the graph structure estimation model of the embodiment. The computer program can be recorded on, for example, a computer-readable storage medium, loaded into the above-mentioned computing device through the computer-readable storage medium, and executed therein.

In the embodiment of the present invention, a graph structure estimation model is proposed, which is composed of a graph prediction model and a graph estimator. In the process of optimizing the graph structure estimation model, the graph prediction model in the graph structure estimation model can be invoked to perform prediction processing on the initial graph to obtain observation information corresponding to the initial graph, where the observation information includes the corresponding initial graph. The prediction information of Prediction information; optimize the graph prediction model based on the prediction information corresponding to the estimated graph and the label information corresponding to the initial graph.

It can be seen from the above process that the optimization of the graph prediction model is not only based on the initial graph and the label information corresponding to the initial graph, but also optimizes the graph prediction model based on the estimated graph. The estimated graph is obtained by estimating the observation information obtained by the graph estimator predicting the initial graph based on the graph prediction model. In other words, the estimated graph is obtained by observing the initial graph from the perspective of the graph prediction model, that is to say, the estimated graph better matches the properties of the graph prediction model than the initial graph, which is more in line with the graph structure. Estimate the properties of the model. Therefore, optimizing the training of the graph prediction model based on the estimated graph can improve the accuracy of the graph prediction model, thereby improving the accuracy of the graph structure estimation model.

Based on the above method and apparatus embodiment, the embodiment of the present invention further provides a training device for a graph structure estimation model. Referring to FIG. 11 , it is a schematic structural diagram of a training device for a graph structure estimation model provided by an embodiment of the present invention. The training device shown in FIG. 11 may include at least a processor 1101 , an input interface 1102 , an output interface 1103 , and a computer storage medium 1104 . Wherein, the processor 1101, the input interface 1102, the output interface 1103 and the computer storage medium 1104 may be connected by a bus or other means.

The computer storage medium 1104 can be stored in the memory of the training device of the graph structure estimation model, the computer storage medium 901 is used to store a computer program, the computer program includes a computer program, and the processor 901 is used to execute the computer storage The computer program stored by the medium 1104 . The processor 1101 (or called CPU (Central Processing Unit, central processing unit)) is the computing core and the control core of the training device of the graph structure estimation model, which is suitable for implementing a computer program, and is specifically suitable for loading and executing:

Obtain the initial graph and the label information corresponding to the initial graph; the initial graph includes multiple nodes, and the label information is used to indicate the category to which the target node in the initial graph belongs, and the target node is a plurality of nodes in the initial graph. Any one or more of the nodes; call the graph prediction model included in the graph structure estimation model to perform prediction processing on the initial graph, and obtain the observation information corresponding to the initial graph; call the graph estimator included in the graph structure estimation model Perform estimation processing based on the label information and the observation information to obtain an estimated graph; and call the graph prediction model to perform prediction processing on the estimated graph to obtain prediction information corresponding to the estimated graph, and the prediction corresponding to the estimated graph The information is used to indicate the category to which each node in the estimation graph belongs; the graph prediction model is optimized based on the prediction information corresponding to the estimation graph and the label information.

In the embodiment of the present invention, a graph structure estimation model is proposed, which is composed of a graph prediction model and a graph estimator. In the process of optimizing the graph structure estimation model, the graph prediction model in the graph structure estimation model can be invoked to perform prediction processing on the initial graph to obtain observation information corresponding to the initial graph, where the observation information includes the corresponding initial graph. The prediction information of Prediction information; optimize the graph prediction model based on the prediction information corresponding to the estimated graph and the label information corresponding to the initial graph.

It can be seen from the above process that the optimization of the graph prediction model is not only based on the initial graph and the label information corresponding to the initial graph, but also optimizes the graph prediction model based on the estimated graph. The estimated graph is obtained by estimating the observation information obtained by the graph estimator predicting the initial graph based on the graph prediction model. In other words, the estimated graph is obtained by observing the initial graph from the perspective of the graph prediction model, that is to say, the estimated graph better matches the properties of the graph prediction model than the initial graph, which is more in line with the graph structure. Estimate the properties of the model. Therefore, optimizing the training of the graph prediction model based on the estimated graph can improve the accuracy of the graph prediction model, thereby improving the accuracy of the graph structure estimation model.

An embodiment of the present invention also provides a computer storage medium (Memory), where the computer storage medium is a memory device in a training device for a graph structure estimation model, and is used to store programs and data. It can be understood that the computer storage medium here may include both the built-in storage medium of the training device of the graph structure estimation model, and of course the extended storage medium supported by the training device of the graph structure estimation model. The computer storage medium provides storage space in which the operating system of the training device of the graph structure estimation model is stored. In addition, a computer program suitable for being loaded and executed by the processor 901 is also stored in this storage space; or a computer program suitable for being loaded and executed by the processor 1101, and these computer programs may be more than one computer program (including a program code). It should be noted that the computer storage medium here can be a high-speed RAM memory, or a non-volatile memory (non-volatile memory), such as at least one disk memory; optionally, it can also be at least one memory located far away from the aforementioned processor. computer storage media.

In one embodiment, the computer storage medium can be loaded by the processor 1101 and execute the computer program stored in the computer storage medium, so as to implement the above-mentioned corresponding steps of the training method for the graph structure estimation model shown in FIG. 3 . In a specific implementation, the computer program in the computer storage medium is loaded by the processor 1101 and performs the following steps:

Obtain the initial graph and the label information corresponding to the initial graph; the initial graph includes multiple nodes, and the label information is used to indicate the category to which the target node in the initial graph belongs, and the target node is a plurality of nodes in the initial graph. Any one or more of the nodes; call the graph prediction model included in the graph structure estimation model to perform prediction processing on the initial graph, and obtain the observation information corresponding to the initial graph; call the graph estimator included in the graph structure estimation model Perform estimation processing based on the label information and the observation information to obtain an estimated graph; and call the graph prediction model to perform prediction processing on the estimated graph to obtain prediction information corresponding to the estimated graph, and the prediction corresponding to the estimated graph The information is used to indicate the category to which each node in the estimation graph belongs; the graph prediction model is optimized based on the prediction information corresponding to the estimation graph and the label information.

In one embodiment, the processor 1101 is further configured to execute: if the end training event is not detected, obtain a corresponding image of the estimated graph obtained in the process of invoking the graph prediction model to perform prediction processing on the estimated graph Observation information; call the graph estimator to perform estimation processing based on the label information and the observation information corresponding to the estimated graph to obtain a new estimated graph, and call the optimized graph prediction model to perform prediction processing on the new estimated graph to obtain the prediction information corresponding to the new estimation graph, and the prediction information corresponding to the new estimation graph is used to indicate the category to which each node in the new estimation graph belongs; based on the prediction information corresponding to the new estimation graph and The label information updates the optimized graph prediction model.

In one embodiment, the observation information includes prediction information corresponding to the initial graph and an observation graph set corresponding to the initial graph, and the prediction information corresponding to the initial graph is used to indicate that each node in the initial graph belongs to category, the observation graph set includes the initial graph and the neighbor graph set corresponding to the initial graph; the graph prediction model includes a first convolutional layer and a second convolutional layer; the processor 1101 is in the Call the graph prediction model included in the graph structure estimation model to perform prediction processing on the initial graph, and when the observation information corresponding to the initial graph is obtained, perform the following steps:

Obtain the node feature matrix of the initial graph, and input the node feature matrix to the first convolutional layer to perform a convolution operation based on the first weight parameter corresponding to the first convolutional layer to obtain the first convolutional layer. A node representation matrix corresponding to a convolutional layer;

Inputting the node representation matrix corresponding to the first convolutional layer to the second convolutional layer to perform a convolution operation based on the second weight parameter corresponding to the second convolutional layer to obtain a second volume The node representation matrix corresponding to the product layer; the node representation matrix corresponding to the second convolution layer is normalized to obtain the prediction information corresponding to the initial graph; based on the node representation corresponding to the first convolution layer The matrix constructs a first neighbor graph, and a second neighbor graph is constructed based on the node representation matrix corresponding to the second convolution layer, and a target neighbor graph is constructed based on the node feature matrix of the initial graph; the first neighbor graph is , the second neighbor graph and the target neighbor graph form the neighbor graph set.

In one embodiment, the graph estimator includes a structure sub-model and an observation sub-model; the processor 1101 performs estimation based on the label information and the observation information when invoking the graph estimator included in the graph structure estimation model When processing the estimated graph, perform the following steps:

Invoke the structural sub-model to generate N candidate graphs based on the label information and the prediction information corresponding to the initial graph in the observation information corresponding to the initial graph, where N is an integer greater than or equal to 1; and based on the structural sub-model The first parameter of and the adjacency matrix corresponding to each candidate image in the N candidate images determine the generation probability corresponding to the corresponding candidate image;

Calling the observation sub-model to calculate the existence probability of the observation information corresponding to the corresponding candidate graph based on the second parameter of the observation sub-model, the observation information corresponding to the initial graph, and the adjacency matrix corresponding to each candidate graph; wherein, The existence probability of the observation information corresponding to the candidate map m is used to indicate that when the candidate map m is used as the estimated map, the probability of the existence of the observation information, m is greater than or equal to 1 and less than or equal to N; The estimated adjacency matrix is obtained by performing graph estimation on the generation probability of , and the existence probability of observation information corresponding to each candidate graph, and the estimated graph is generated according to the estimated adjacency matrix.

In one embodiment, the N candidate graphs include a first candidate graph, and the processor 1101 calls the observation sub-model based on the second parameter of the observation sub-model, observation information corresponding to the initial graph, and For the adjacency matrix corresponding to each candidate graph, when calculating the existence probability of the observation information corresponding to the corresponding candidate graph, the following steps are performed:

Acquiring the total number of data included in the observation information, and determining an observation probability parameter according to the second parameter; acquiring the first quantity of data indicating the existence of an edge between node i and node j in the observation information, and determining the observation probability parameter according to the second parameter; The first quantity and the total quantity determine the second quantity of data indicating that there is no edge between node i and node j in the observation information; wherein, node i and node j are any arbitrary data included in the first candidate graph. Two nodes and i is less than j; calculate the edge correlation probability between the node i and node j according to the observation probability parameter, the first number and the second number; The edge correlation probabilities between the nodes are multiplied to obtain the existence probability of the observation information corresponding to the first candidate graph.

In one embodiment, the observation probability parameter includes a first-type parameter, a second-type parameter, a third-type parameter, and a fourth-type parameter; wherein, the first-type parameter refers to the time between node i and node j When there is an edge, any data in the observation set indicates the probability of the existence of an edge between the node i and node j; the second type of parameter refers to the observation when an edge exists between node i and node j Any data in the set indicates the probability that the edge between node i and node j does not exist; the third type of parameter refers to when there is no edge between node i and node j, any data in the observation set Indicates the probability that the edge between the node i and the node j does not exist, and the fourth parameter refers to when there is no edge between the node i and the node j, any data in the observation set indicates that the node i and the probability that an edge exists between node j.

In one embodiment, the N candidate pictures include a first candidate picture and a second candidate picture, and the processor 1101 is based on the generation probability corresponding to each candidate picture and the existence probability of observation information corresponding to each candidate picture. When performing graph estimation to obtain an estimated adjacency matrix, perform the following steps:

Obtain the probability of the first parameter and the probability of the second parameter; combine the probability of the first parameter, the probability of the second parameter, and the corresponding generation probability of the first candidate map with the first candidate The existence probability of the observation information corresponding to the graph is input into the candidate probability calculation rule for calculation, and the first candidate graph is obtained as the first candidate probability of the estimated graph; the probability of the first parameter, the probability of the second parameter and the The generation probability corresponding to the second candidate picture and the existence probability of the observation information corresponding to the second candidate picture are input into the candidate probability calculation rule for calculation, and the second candidate picture is obtained as the second candidate probability of the estimated picture generating an estimated adjacency matrix based on the first candidate probability, the adjacency matrix corresponding to the first candidate graph, the second candidate probability and the adjacency matrix corresponding to the second candidate graph.

In one embodiment, the adjacency matrix corresponding to any candidate graph includes M rows and M columns, the adjacency matrix corresponding to any candidate graph includes M by M matrix elements, and the estimated adjacency matrix includes M rows and M columns, so The estimated adjacency matrix includes M by M target matrix elements; the processor 1101 is based on the first candidate probability, the adjacency matrix corresponding to the first candidate map, the second candidate probability and the second candidate When generating the estimated adjacency matrix from the adjacency matrix corresponding to the graph, perform the following steps:

Obtain the first matrix element at the position of the ith row and the jth column in the adjacency matrix corresponding to the first candidate image, and obtain the second element at the position of the ith row and the jth column in the adjacency matrix corresponding to the second candidate image. matrix element; multiply the first matrix element and the first candidate probability to obtain a first operation result, and multiply the second matrix element and the second candidate probability to obtain the first operation result. Two operation results; performing an addition operation on the first operation result and the second operation result, and the operation result is used as the target matrix element at the position of the i-th row and the j-th column in the estimated adjacency matrix.

In one embodiment, after generating an estimated adjacency matrix based on the first candidate probability, the adjacency matrix corresponding to the first candidate graph, the second candidate probability, and the adjacency matrix corresponding to the second candidate graph, the The processor 1101 is also used to execute:

The first parameter and the second parameter are optimized according to the first candidate probability and the second candidate probability; the adjacency matrix is estimated based on the optimized first parameter and the optimized second parameter pair Perform update processing.

In one embodiment, when the processor 1101 performs optimization processing on the first parameter and the second parameter according to the first candidate probability and the second candidate probability, the following steps are performed:

The first candidate probability and the second candidate probability are added to obtain a joint posterior probability expression of the first parameter and the second parameter; the joint posterior probability is calculated by using a preset inequality Transform the expression; perform a derivation operation on the transformed joint posterior probability based on the first parameter to obtain an optimization equation corresponding to the first parameter, and perform a derivation operation on the changed joint posterior based on the second parameter Perform a derivation operation on the probability to obtain the optimization equation corresponding to the second parameter; solve the optimization equation corresponding to the first parameter to obtain the optimized first parameter, and the optimization corresponding to the second parameter, etc. The second parameter after optimization is obtained by solving the formula.

In one embodiment, when the processor 1101 generates the estimated graph according to the estimated adjacency matrix, the following steps are performed:

Perform sparse processing on the estimated adjacency matrix, and extract a target adjacency matrix from the estimated adjacency matrix; and generate the estimated graph according to the target adjacency matrix.

In one embodiment, when the processor 1101 performs sparse processing on the estimated adjacency matrix and extracts a target adjacency matrix from the estimated adjacency matrix, the processor 1101 performs the following steps: traversing each target in the estimated adjacency matrix Matrix elements, replace the matrix elements less than or equal to the threshold value in the estimated adjacency matrix to zero to obtain the target adjacency matrix.

In one embodiment, the prediction information corresponding to the initial graph includes a predicted value corresponding to each node in the multiple nodes of the initial graph, and the predicted value corresponding to any node is used to indicate the category to which any node belongs, The label information includes a target value used to indicate the category to which the target node belongs. After the first neighbor graph and the second neighbor graph are formed into the neighbor graph set, the processor 1101 is further configured to:

Obtain the predicted value corresponding to the target node from the prediction information corresponding to the initial graph, and determine the difference information between the predicted value corresponding to the target node and the target value included in the label information; according to the constructing a loss function corresponding to the graph prediction model based on the difference information; updating the first weight parameter and the second weight parameter in the direction of reducing the value of the loss function; based on the updated first weight parameter and the updated second weight parameter The weight parameter updates the prediction information corresponding to the initial graph and the neighbor graph set respectively.

In one embodiment, the processor 1101 is further configured to: acquire the graph to be processed, and call the optimized graph prediction model in the graph structure estimation model to perform prediction processing on the graph to be processed, and obtain the graph to be processed target observation information corresponding to the graph, where the target observation information includes target prediction information corresponding to the graph to be processed; call the graph estimator to perform estimation processing based on the target observation information to obtain a target estimation graph; call the graph prediction model The target estimation graph is processed to obtain a prediction result corresponding to the target estimation graph, where the prediction result is used to indicate the category to which each node in the to-be-processed graph belongs.

In the embodiment of the present invention, a graph structure estimation model is proposed, which is composed of a graph prediction model and a graph estimator. In the process of optimizing the graph structure estimation model, the graph prediction model in the graph structure estimation model can be invoked to perform prediction processing on the initial graph to obtain observation information corresponding to the initial graph, where the observation information includes the corresponding initial graph. The prediction information of Prediction information; optimize the graph prediction model based on the prediction information corresponding to the estimated graph and the label information corresponding to the initial graph.

It can be seen from the above process that the optimization of the graph prediction model is not only based on the initial graph and the label information corresponding to the initial graph, but also optimizes the graph prediction model based on the estimated graph. The estimated graph is obtained by estimating the observation information obtained by the graph estimator predicting the initial graph based on the graph prediction model. In other words, the estimated graph is obtained by observing the initial graph from the perspective of the graph prediction model, that is to say, the estimated graph better matches the properties of the graph prediction model than the initial graph, which is more in line with the graph structure. Estimate the properties of the model. Therefore, optimizing the training of the graph prediction model based on the estimated graph can improve the accuracy of the graph prediction model, thereby improving the accuracy of the graph structure estimation model.

According to an aspect of the present application, an embodiment of the present invention further provides a computer program product or a computer program, where the computer program product includes a computer program, and the computer program is stored in a computer storage medium. The processor 1101 reads the computer program from the computer storage medium, and the processor 1101 executes the computer program, so that the training device executes the training method of the graph structure estimation model as shown in Figure 3 and Figure 5, specifically:

Obtain the initial graph and the label information corresponding to the initial graph; the initial graph includes multiple nodes, and the label information is used to indicate the category to which the target node in the initial graph belongs, and the target node is a plurality of nodes in the initial graph. Any one or more of the nodes; call the graph prediction model included in the graph structure estimation model to perform prediction processing on the initial graph, and obtain the observation information corresponding to the initial graph; call the graph estimator included in the graph structure estimation model Perform estimation processing based on the label information and the observation information to obtain an estimated graph; and call the graph prediction model to perform prediction processing on the estimated graph to obtain prediction information corresponding to the estimated graph, and the prediction corresponding to the estimated graph The information is used to indicate the category to which each node in the estimation graph belongs; the graph prediction model is optimized based on the prediction information corresponding to the estimation graph and the label information.

Claims (15)

1. A method for training a graph structure estimation model, comprising:

acquiring an initial graph and label information corresponding to the initial graph; the initial graph comprises a plurality of nodes, the label information is used for indicating the category of a target node in the initial graph, and the target node is any one or more of the plurality of nodes of the initial graph;

calling a graph prediction model included in a graph structure estimation model to perform prediction processing on the initial graph to obtain observation information corresponding to the initial graph;

calling a graph estimator included in the graph structure estimation model to perform estimation processing based on the label information and the observation information to obtain an estimation graph; calling the graph prediction model to perform prediction processing on the estimation graph to obtain prediction information corresponding to the estimation graph, wherein the prediction information corresponding to the estimation graph is used for indicating the category of each node in the estimation graph;

and optimizing the graph prediction model based on the prediction information corresponding to the estimation graph and the label information.

2. The method of claim 1, wherein after optimizing the graph prediction model based on the prediction information corresponding to the estimation graph and the label information, the method further comprises:

if the training ending event is not detected, acquiring observation information corresponding to the estimation graph obtained in the process of calling the graph prediction model to perform prediction processing on the estimation graph;

calling the graph estimator to perform estimation processing based on the label information and observation information corresponding to the estimation graph to obtain a new estimation graph, calling an optimized graph prediction model to perform prediction processing on the new estimation graph to obtain prediction information corresponding to the new estimation graph, wherein the prediction information corresponding to the new estimation graph is used for indicating the category to which each node in the new estimation graph belongs;

and updating the optimized graph prediction model based on the prediction information corresponding to the new estimation graph and the label information.

3. The method of claim 1, wherein the observation information comprises prediction information corresponding to the initial graph and an observation graph set corresponding to the initial graph, the prediction information corresponding to the initial graph is used for the observation information, and the observation graph set comprises the initial graph and a neighbor graph set corresponding to the initial graph; the method for predicting the initial graph by using the graph structure estimation model comprises the following steps of:

acquiring a node characteristic matrix of the initial graph, inputting the node characteristic matrix into the first convolutional layer, and performing convolution operation based on a first weight parameter corresponding to the first convolutional layer to obtain a node representation matrix corresponding to the first convolutional layer;

inputting the node representation matrix corresponding to the first convolutional layer into the second convolutional layer to perform convolution operation based on a second weight parameter corresponding to the second convolutional layer to obtain a node representation matrix corresponding to the second convolutional layer;

normalizing the node expression matrix corresponding to the second convolution layer to obtain the prediction information corresponding to the initial graph;

constructing a first neighbor graph based on the node representation matrix corresponding to the first convolutional layer, constructing a second neighbor graph based on the node representation matrix corresponding to the second convolutional layer, and constructing a target neighbor graph based on the node feature matrix of the initial graph;

forming the first neighbor graph, the second neighbor graph, and the target neighbor graph into the set of neighbor graphs.

4. The method of claim 3, wherein the graph estimator comprises a structure submodel and an observation submodel, and wherein invoking the graph structure estimation model comprises the graph estimator performing an estimation process based on the label information and the observation information to obtain an estimated graph, comprising:

calling the structure submodel to generate N candidate graphs based on the label information and the prediction information corresponding to the initial graph in the observation information corresponding to the initial graph, wherein N is an integer greater than or equal to 1; determining the generation probability corresponding to the corresponding candidate graph based on the first parameter of the structure submodel and the adjacency matrix corresponding to each candidate graph in the N candidate graphs;

calling the observation submodel to calculate the existence probability of the observation information corresponding to the corresponding candidate graph based on the second parameter of the observation submodel, the observation information corresponding to the initial graph and the adjacency matrix corresponding to each candidate graph; wherein, the observation information existence probability corresponding to the candidate map m is used for representing the probability of existence of the observation information when the candidate map m is taken as the estimation map, and m is greater than or equal to 1 and less than or equal to N;

and carrying out graph estimation based on the generation probability corresponding to each candidate graph and the observation information existence probability corresponding to each candidate graph to obtain an estimated adjacency matrix, and generating the estimated graph according to the estimated adjacency matrix.

5. The method of claim 4, wherein the N candidate graphs include a first candidate graph, and wherein the invoking the observation submodel calculates the probability of existence of the observation information corresponding to the respective candidate graph based on a second parameter of the observation submodel, the observation information corresponding to the initial graph, and the adjacency matrix corresponding to each candidate graph, comprises:

acquiring the total amount of data included in the observation information, and determining an observation probability parameter according to the second parameter;

acquiring a first quantity of data indicating that an edge exists between a node i and a node j in the observation information, and determining a second quantity of data indicating that an edge does not exist between the node i and the node j in the observation information according to the first quantity and the total quantity; the node i and the node j are any two nodes included in the first candidate graph, and i is smaller than j;

calculating the edge correlation probability between the node i and the node j according to the observation probability parameter, the first quantity and the second quantity;

and multiplying the edge correlation probabilities between every two nodes in the first candidate graph to obtain the existence probability of the observation information corresponding to the first candidate graph.

6. The method of claim 5, wherein the observation probability parameters include a first class of parameters, a second class of parameters, a third class of parameters, and a fourth class of parameters; the first type of parameter refers to the probability that any data in the observation set indicates the existence of an edge between a node i and a node j when the edge exists between the node i and the node j; the second type of parameter refers to the probability that any data in the observation set indicates that an edge does not exist between a node i and a node j when the edge exists between the node i and the node j; the third type of parameter refers to a probability that any data in the observation set indicates that an edge does not exist between the node i and the node j when the edge does not exist between the node i and the node j, and the fourth type of parameter refers to a probability that any data in the observation set indicates that an edge does not exist between the node i and the node j when the edge does not exist between the node i and the node j.

7. The method of claim 4, wherein the N candidate maps include a first candidate map and a second candidate map, and wherein the performing the map estimation based on the generation probability corresponding to each candidate map and the observation information existence probability corresponding to each candidate map to obtain the estimated adjacency matrix comprises:

acquiring the probability of the first parameter and the probability of the second parameter;

inputting the probability of the first parameter, the probability of the second parameter, the generation probability corresponding to the first candidate graph and the observation information existence probability corresponding to the first candidate graph into a candidate probability calculation rule for operation to obtain a first candidate probability of the first candidate graph as an estimation graph;

inputting the probability of the first parameter, the probability of the second parameter, the generation probability corresponding to the second candidate graph and the observation information existence probability corresponding to the second candidate graph into the candidate probability calculation rule for operation to obtain a second candidate probability of the second candidate graph as an estimation graph;

and generating an estimated adjacency matrix based on the first candidate probability, the adjacency matrix corresponding to the first candidate graph, the second candidate probability and the adjacency matrix corresponding to the second candidate graph.

8. The method of claim 7, wherein the adjacency matrix for any candidate comprises M rows and M columns, the adjacency matrix for any candidate comprises M by M matrix elements, the estimated adjacency matrix comprises M rows and M columns, and the estimated adjacency matrix comprises M by M target matrix elements; the generating an estimated adjacency matrix based on the first candidate probability, the adjacency matrix corresponding to the first candidate graph, the second candidate probability, and the adjacency matrix corresponding to the second candidate graph includes:

acquiring a first matrix element at the jth row and jth column position in an adjacent matrix corresponding to the first candidate map, and acquiring a second matrix element at the jth row and jth column position in the adjacent matrix corresponding to the second candidate map;

multiplying the first matrix element by the first candidate probability to obtain a first operation result, and multiplying the second matrix element by the second candidate probability to obtain a second operation result;

and performing addition operation on the first operation result and the second operation result, wherein the operation result is used as a target matrix element at the ith row and jth column position in the estimated adjacent matrix.

9. The method of claim 7, wherein after generating an estimated adjacency matrix based on the first candidate probability, the adjacency matrix corresponding to the first candidate graph, the second candidate probability, and the adjacency matrix corresponding to the second candidate graph, the method further comprises:

optimizing the first parameter and the second parameter according to the first candidate probability and the second candidate probability;

and updating the estimated adjacency matrix based on the optimized first parameter and the optimized second parameter.

10. The method of claim 9, wherein the optimizing the first parameter and the second parameter based on the first candidate probability and the second candidate probability comprises:

adding the first candidate probability and the second candidate probability to obtain a combined posterior probability expression of the first parameter and the second parameter;

transforming the combined posterior probability expression by using a preset inequality;

performing derivation operation on the transformed joint posterior probability based on the first parameter to obtain an optimization equation corresponding to the first parameter, and performing derivation operation on the transformed joint posterior probability based on the second parameter to obtain an optimization equation corresponding to the second parameter;

and solving the optimization equation corresponding to the first parameter to obtain the optimized first parameter, and solving the optimization equation corresponding to the second parameter to obtain the optimized second parameter.

11. The method of claim 4, wherein the generating the estimate map from the estimate adjacency matrix comprises:

carrying out sparsification processing on the estimated adjacency matrix, and extracting a target adjacency matrix from the estimated adjacency matrix;

and generating the estimation graph according to the target adjacency matrix.

12. The method of claim 11, wherein the sparsifying of the estimated adjacency matrix and extracting a target adjacency matrix from the estimated adjacency matrix comprises:

traversing each target matrix element in the estimated adjacency matrix, and replacing matrix elements smaller than or equal to a threshold value in the estimated adjacency matrix with zeros to obtain the target adjacency matrix.

13. The method of claim 3, wherein the prediction information corresponding to the initial graph comprises a prediction value corresponding to each node in a plurality of nodes of the initial graph, the prediction value corresponding to any node is used for indicating a category to which the any node belongs, the label information comprises a target value used for indicating a category to which a target node belongs, and after the first neighbor graph and the second neighbor graph are combined into the neighbor graph set, the method further comprises:

obtaining a predicted value corresponding to the target node from the predicted information corresponding to the initial graph, and determining difference information between the predicted value corresponding to the target node and the target value included in the tag information;

constructing a loss function corresponding to the graph prediction model according to the difference information;

updating the first weight parameter and the second weight parameter in a direction of decreasing the value of the penalty function;

and updating the prediction information corresponding to the initial graph and the neighbor graph set respectively based on the updated first weight parameter and the updated second weight parameter.

14. The method of claim 1, wherein the method further comprises:

obtaining a graph to be processed, calling the graph prediction model optimized in the graph structure estimation model to perform prediction processing on the graph to be processed, and obtaining target observation information corresponding to the graph to be processed, wherein the target observation information comprises target prediction information corresponding to the graph to be processed;

calling the graph estimator to perform estimation processing based on the target observation information to obtain a target estimation graph;

and calling the graph prediction model to process the target estimation graph to obtain a prediction result corresponding to the target estimation graph, wherein the prediction result is used for indicating the category of each node in the graph to be processed.

15. A model processing apparatus, comprising:

the device comprises an acquisition unit, a processing unit and a processing unit, wherein the acquisition unit is used for acquiring an initial graph and label information corresponding to the initial graph; the initial graph comprises a plurality of nodes, the label information is used for indicating the category of a target node in the initial graph, and the target node is any one or more of the plurality of nodes of the initial graph;

the processing unit is used for calling a graph prediction model included in a graph structure estimation model to perform prediction processing on the initial graph to obtain observation information corresponding to the initial graph, wherein the observation information includes prediction information corresponding to the initial graph, and the prediction information corresponding to the initial graph is used for indicating the category of each node in the initial graph;

the processing unit is further configured to invoke a graph estimator included in the graph structure estimation model to perform estimation processing based on the label information and the observation information to obtain an estimation graph; calling the graph prediction model to perform prediction processing on the estimation graph to obtain prediction information corresponding to the estimation graph, wherein the prediction information corresponding to the estimation graph is used for indicating the category of each node in the estimation graph;

the processing unit is further configured to optimize the graph prediction model based on prediction information corresponding to the estimation graph and the label information.

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