CN106295797A

CN106295797A - A kind of FNR based on random weight network analyzes training method and the training system of model

Info

Publication number: CN106295797A
Application number: CN201610652065.3A
Authority: CN
Inventors: 何玉林; 王熙照; 黄哲学
Original assignee: Shenzhen University
Current assignee: Shenzhen University
Priority date: 2016-08-10
Filing date: 2016-08-10
Publication date: 2017-01-04

Abstract

The invention relates to the technical field of data analysis, in particular to a training method and a training system for an FNR (Fuzzy Nonlinear Regression, fuzzy nonlinear regression) analysis model based on a random weight network. The random weight network used in the training method and training system does not need iterative training, its input weight is randomly selected, and the output weight is obtained analytically based on the training set of fuzzy input-fuzzy output, and through the analytical expression of the output layer weight regularization to control the overfitting of the model. Compared with the traditional FNR model based on Sigmoid neural network and the FNR model based on radial basis function network, the advantages of the present invention are as follows: extremely fast training speed (nearly 1000 times faster than existing methods) and efficient Over-fitting control ability (basically no over-fitting phenomenon).

Description

A kind of training method and training system of FNR analysis model based on random weight network

技术领域technical field

本发明涉及数据分析技术领域，尤其涉及一种基于随机权网络的FNR(FuzzyNonlinear Regression，模糊非线性回归)分析模型的训练方法及训练系统。The invention relates to the technical field of data analysis, in particular to a training method and a training system for an FNR (Fuzzy Nonlinear Regression, fuzzy nonlinear regression) analysis model based on a random weight network.

背景技术Background technique

模糊回归分析分为模糊线性回归(Fuzzy Linear Regression-FLR)分析和FNR(Fuzzy Nonlinear Regression-FNR)分析两种。1982年，日本学者Tanaka等人[1]给出了最早的FLR分析模型：清晰输入与模糊输出之间的关系通过构建一个带有模糊系数的线性函数来表示。之后，大批学者对Tanaka的FLR模型进行了扩展，主要包括两个方面：带有清晰系数的模糊输入-模糊输出FLR模型和带有模糊系数的模糊输入-模糊输出FLR模型。求解FLR模型的主要任务就是确定线性函数中的清晰系数或者模糊系数。常用的方法包括目标规划法(Goal Programming Approach)和模糊最小二乘法(Fuzzy Least Square Method)。然而，对于大多数的实际应用而言，输入与输出之间的关系往往是非线性的。显然，Tanaka的FLR模型以及之后的FLR改进模型不能够处理非线性模糊输入-模糊输出的回归问题。鉴于神经网络在处理非线性回归问题上的优势，1995年日本学者Ishibuchi等人[2]以及2005年Zhang等人[3]分别提出使用Sigmoid神经网络和径向基函数网络处理非线性模糊输入-模糊输出回归问题的FNR模型FNRBP和FNRRBF，其中Sigmoid神经网络的输入层和输出层权重以及径向基函数网络的径向基函数中心、半径以及输出层权重均采用迭代式的、基于梯度下降的误差反传方法确定。尽管FNRBP和FNRRBF获得了良好的实验效果，但是较高的计算复杂度以及模型的易过拟合在很大程度上限制了FNRBP和FNRRBF向实际应用领域的推广。Fuzzy regression analysis is divided into fuzzy linear regression (Fuzzy Linear Regression-FLR) analysis and FNR (Fuzzy Nonlinear Regression-FNR) analysis. In 1982, Japanese scholar Tanaka et al. [1] gave the earliest FLR analysis model: the relationship between clear input and fuzzy output is expressed by constructing a linear function with fuzzy coefficients. Later, a large number of scholars extended Tanaka's FLR model, which mainly includes two aspects: the fuzzy input-fuzzy output FLR model with clear coefficients and the fuzzy input-fuzzy output FLR model with fuzzy coefficients. The main task of solving the FLR model is to determine the sharp or fuzzy coefficients in the linear function. Commonly used methods include Goal Programming Approach and Fuzzy Least Square Method. However, for most practical applications, the relationship between input and output is often nonlinear. Obviously, Tanaka's FLR model and the subsequent FLR improved model cannot deal with the nonlinear fuzzy input-fuzzy output regression problem. In view of the advantages of neural networks in dealing with nonlinear regression problems, Japanese scholars Ishibuchi et al. [2] in 1995 and Zhang et al. [3] in 2005 proposed to use Sigmoid neural network and radial basis function network to deal with nonlinear fuzzy input- The FNR models FNRBP and FNRRBF of the fuzzy output regression problem, in which the input layer and output layer weights of the Sigmoid neural network and the radial basis function center, radius and output layer weights of the radial basis function network all adopt iterative, gradient-based The error backpropagation method is determined. Although FNRBP and FNRRBF have obtained good experimental results, the high computational complexity and the easy overfitting of the model largely limit the promotion of FNRBP and FNRRBF to practical applications.

FNR分析是一种有效的、用于分析模糊输入-模糊输出变量之间非线性函数关系的数据挖掘技术，已被成功地应用于商业管理、工程控制、经济学、社会学、以及生物科学等领域，获得了良好的实际应用效果。现有的解决FNR问题的主要策略是利用迭代式的误差反传算法训练Sigmoid神经网络或者是径向基函数网络，这两种策略的主要缺陷表现在：训练复杂度较高以及模型易过拟合。FNR analysis is an effective data mining technique for analyzing the nonlinear functional relationship between fuzzy input-fuzzy output variables, and has been successfully applied in business management, engineering control, economics, sociology, and biological sciences, etc. field, and achieved good practical application results. The existing main strategy to solve the FNR problem is to use the iterative error backpropagation algorithm to train the Sigmoid neural network or the radial basis function network. The main defects of these two strategies are: high training complexity and easy overfitting of the model combine.

现有的使用神经网络解决非线性模糊输入-模糊输出回归问题的主要方法包括以下两种：基于Sigmoid神经网络的FNR模型FNR_BP和基于径向基函数网络的FNR模型FNR_RBF。The existing main methods of using neural network to solve nonlinear fuzzy input-fuzzy output regression problem include the following two: FNR model FNR _BP based on Sigmoid neural network and FNR model FNR _RBF based on radial basis function network.

FNR_BP为一个三层全链接前馈式神经网络，隐含层节点的激活函数为Sigmoid函数，输入层权重、隐含层偏置、以及输出层权重均为清晰值，用于处理输入和输出均为区间值模糊数的非线性模糊回归问题。FNR_BP基于梯度下降法推导出权重的更新规则，之后使用误差反传方法迭代地调整网络权重，从而使得预测误差最小化。FNR _BP is a three-layer full-link feed-forward neural network. The activation function of the hidden layer nodes is the Sigmoid function. The input layer weights, hidden layer biases, and output layer weights are all clear values for processing input and output. Both are nonlinear fuzzy regression problems with interval-valued fuzzy numbers. FNR _BP derives the weight update rule based on the gradient descent method, and then uses the error backpropagation method to iteratively adjust the network weight to minimize the prediction error.

FNR_RBF为一个输入和输出均为L-R型模糊数的径向基函数网络，其径向基函数的中心、半径、以及输出层权重均为L-R型模糊数。类似于FNR_BP，FNR_RBF同样采用梯度下降法推导出权重的更新规则，之后再使用误差反传方法迭代地调整网络参数，从而达到最小化预测误差的目的。FNR _RBF is a radial basis function network whose input and output are LR-type fuzzy numbers, and the center, radius, and output layer weight of the radial basis function are all LR-type fuzzy numbers. Similar to FNR _BP , FNR _RBF also uses the gradient descent method to derive the update rule of the weight, and then uses the error back propagation method to iteratively adjust the network parameters, so as to minimize the prediction error.

上述基于Sigmoid神经网络的FNR模型FNR_BP和基于径向基函数网络的FNR模型FNR_RBF的主要缺点为：The main disadvantages of the above-mentioned FNR model FNR _BP based on the Sigmoid neural network and the FNR model FNR _RBF based on the radial basis function network are:

时间复杂度高：由于采用了基于梯度下降的迭代式参数调整策略，为了保证预测误差的最小化，模型的训练往往需要几百次乃至上千次的迭代，因此FNR_BP和FNR_RBF的训练非常耗时；High time complexity: Due to the use of an iterative parameter adjustment strategy based on gradient descent, in order to ensure the minimization of prediction errors, the training of the model often requires hundreds or even thousands of iterations, so the training of FNR _BP and FNR _RBF is very difficult. time consuming;

易过拟合：过拟合是神经网络最为显著的缺陷，当使用神经网络处理非线性模糊输入-模糊输出回归问题时，这一缺陷同样不可避免。当使用误差反传算法在训练训练样本上获得了神经网络的最优参数后，神经网络很容易陷入一种“饱和”的状态，即来自于训练集的知识使神经网络的知识库充满，从而无法接受新知识。Easy to overfitting: Overfitting is the most obvious defect of neural networks, and this defect is also inevitable when using neural networks to deal with nonlinear fuzzy input-fuzzy output regression problems. After using the error backpropagation algorithm to obtain the optimal parameters of the neural network on the training samples, the neural network can easily fall into a state of "saturation", that is, the knowledge from the training set fills the knowledge base of the neural network, thus Unable to accept new knowledge.

发明内容Contents of the invention

本发明所要解决的技术问题是，提供一种基于随机权网络的FNR分析模型的训练方法及训练系统，以解决现有的基于Sigmoid神经网络的FNR分析模型和基于径向基函数网络的FNR分析模型时间复杂度高、且易于过拟合的缺陷。本发明是这样实现的：The technical problem to be solved by the present invention is to provide a kind of training method and training system based on the FNR analysis model of random weight network, to solve the existing FNR analysis model based on Sigmoid neural network and the FNR analysis based on radial basis function network The model has high time complexity and is prone to overfitting defects. The present invention is achieved like this:

一种基于随机权网络的FNR分析模型的训练方法，包括如下步骤：A kind of training method of the FNR analysis model based on random weight network, comprises the steps:

步骤1：确定用以引导随机权网络隐含层输出权重的训练模式的损失函数E；Step 1: Determine the loss function E of the training mode used to guide the output weight of the hidden layer of the random weight network;

所述损失函数E的表达式如下：The expression of the loss function E is as follows:

其中： in:

N为训练样本数目；N is the number of training samples;

α表示截点值；α represents the cutoff value;

[T_n]_α为训练样本X_n预测输出的α-截集， [T _n ] _α is the α-cut set of the predicted output of the training sample X _n ,

[γ_n]_α为训练样本X_n实际输出的α-截集， [γ _n ] _α is the α-cut set of the actual output of the training sample X _n ,

其中： in:

表示训练样本X_n预测输出的α-截集的下边界点； Represents the lower boundary point of the α-cut set of the training sample X _n predicted output;

表示训练样本X_n预测输出的α-截集的上边界点； Represents the upper boundary point of the α-cut set of the training sample X _n predicted output;

表示训练样本X_n实际输出的α-截集的下边界点； Represents the lower boundary point of the α-cut set actually output by the training sample X _n ;

表示训练样本X_n实际输出的α-截集的上边界点； Represents the upper boundary point of the α-cut set actually output by the training sample X _n ;

步骤2：确定所述训练样本X_n预测输出的α-截集的具体形式为：Step 2: Determine the specific form of the α-cut set of the predicted output of the training sample X _n as:

；其中：;in:

H_nj表示第n个训练样本对应的第j个隐含层节点的输出；H _nj represents the output of the jth hidden layer node corresponding to the nth training sample;

表示H_nj的α‐截集的下边界点； Represents the lower boundary point of the α-cut set of H _nj ;

表示H_nj的α‐截集的上边界点； Represents the upper boundary point of the α-cut set of H _nj ;

r_nj1表示第n个训练样本对应的第j个隐含层节点输入的左端点；r _nj1 represents the left endpoint of the jth hidden layer node input corresponding to the nth training sample;

r_nj2表示第n个训练样本对应的第j个隐含层节点输入的中值点；r _nj2 represents the median point of the jth hidden layer node input corresponding to the nth training sample;

r_nj3表示第n个训练样本对应的第j个隐含层节点输入的右端点；r _nj3 represents the right endpoint of the jth hidden layer node input corresponding to the nth training sample;

β_j表示第j个隐含层节点与输出层节点链接的权重；β _j represents the weight of the link between the jth hidden layer node and the output layer node;

步骤3：根据所述损失函数E确定随机权网络输出层权重β的具体形式；具体为：Step 3: Determine the specific form of the output layer weight β of the random weight network according to the loss function E; specifically:

其中： in:

为随机权网络隐含层输出的α‐截集的下边界矩阵， is the lower boundary matrix of the α-cut set output by the hidden layer of the random weight network,

为随机权网络隐含层输出的α‐截集的上边界矩阵， is the upper boundary matrix of the α-cut set output by the hidden layer of the random weight network,

为实际输出的α‐截集的下边界向量， is the lower boundary vector of the actual output α-cut set,

为实际输出的α‐截集的上边界向量，其中： is the upper boundary vector of the actual output α-cut set, in:

_N×K表示矩阵的阶数为N行K列； _N×K means that the order of the matrix is N rows and K columns;

T表示向量的转置；T represents the transpose of the vector;

根据推导出according to Deduced

其中： in:

为隐含层输出的α‐截集的下边界矩阵的积分， is the integral of the lower bound matrix of the α-cut set output by the hidden layer,

为隐含层输出的α‐截集的上边界矩阵的积分， is the integral of the upper bound matrix of the α-cut set output by the hidden layer,

为实际输出的α‐截集的下边界向量的积分， is the integral of the lower boundary vector of the α-cut set of the actual output,

为实际输出的α‐截集的上边界向量的积分， is the integral of the upper boundary vector of the α-cut set of the actual output,

其中：in:

y_N1表示第N个训练样本实际输出的α‐截集的左端点；y _N1 represents the left endpoint of the α-cut set actually output by the Nth training sample;

y_N2表示第N个训练样本实际输出的α‐截集的中值点；y _N2 represents the median point of the α-cut set actually output by the Nth training sample;

y_N3表示第N个训练样本实际输出的α‐截集的右端点；y _N3 represents the right endpoint of the α-cut set actually output by the Nth training sample;

令则得出随机权网络输出层权重β的解析表达式为：make Then the analytical expression of the weight β of the output layer of the random weight network is obtained as:

β＝H⁺γ；β = H ⁺ γ;

其中，H⁺为矩阵H的广义逆矩阵， Among them, H ⁺ is the generalized inverse matrix of matrix H,

其中，C为正则化因子，用以控制随机权网络的过拟合，C>0；I为单位矩阵。Among them, C is a regularization factor, which is used to control the overfitting of the random weight network, C>0; I is the identity matrix.

进一步地，假设训练样本X_n对应的隐含层输入向量为R_n＝(R_n1，R_n2,…,R_nK)，则第n个训练样本对应的第j个隐含层节点的输入R_nj对应的三角模糊数为：Further, assuming that the hidden layer input vector corresponding to the training sample X _n is R _n =(R _n1 , R _n2 ,...,R _nK ), then the input R of the jth hidden layer node corresponding to the nth training sample The triangular fuzzy number corresponding to _nj is:

其中： in:

w_ji表示模糊随机权网络第i个输入层节点与第j个隐含层节点链接的权重；w _ji represents the weight of the connection between the i-th input layer node and the j-th hidden layer node of the fuzzy random weight network;

x_ni1表示第n个训练样本的左端点；x _ni1 represents the left endpoint of the nth training sample;

x_ni2表示第n个训练样本的中值点；x _ni2 represents the median point of the nth training sample;

x_ni3表示第n个训练样本的右端点；x _ni3 represents the right endpoint of the nth training sample;

利用H_n＝(H_n1，H_n2,…,H_nK)表示训练样本X_n对应的隐含层输出向量，则分量H_nj表示为：Use H _n = (H _n1 , H _n2 ,..., H _nK ) to represent the hidden layer output vector corresponding to the training sample X _n , then the component H _nj is expressed as:

${H h}_{n no j j} = = (({h h}_{n no j j 11},, {h h}_{n no j j 22},, {h h}_{n no j j 33})) = = ((\frac{11}{11 + + exp exp ((- - {r r}_{n no j j 11}))},, \frac{11}{11 + + exp exp ((- - {r r}_{n no j j 22}))},, \frac{11}{11 + + exp exp ((- - {r r}_{n no j j 33}))})) . .$

进一步地，假设未知样本为：Further, suppose the unknown sample is:

X＝(X₁,X₂,…,X_D)＝((x₁₁，x₁₂，x₁₃),(x₂₁，x₂₂，x₂₃),…,(x_D1，x_D2，x_D3))；其中：X=(X ₁ ,X ₂ ,...,X _D )=((x ₁₁ ,x ₁₂ ,x ₁₃ ),(x ₂₁ ,x ₂₂ ,x ₂₃ ),...,(x _D1 ,x _D2 ,x _D3 ) );in:

X为未知样本；X is an unknown sample;

X_D表示未知样本的第D个三角模糊数属性；X _D represents the Dth triangular fuzzy number attribute of the unknown sample;

x_D1表示三角模糊数X_D的左端点；x _D1 represents the left endpoint of the triangular fuzzy number X _D ;

x_D2表示三角模糊数X_D的中值点；x _D2 represents the median point of the triangular fuzzy number X _D ;

x_D3表示三角模糊数X_D的右端点；x _D3 represents the right endpoint of the triangular fuzzy number X _D ;

所述方法还包括：The method also includes:

步骤4：利用训练得到的FNR分析模型对未知样本X进行预测，得到的预测输出的α‐截集表示为：Step 4: Use the trained FNR analysis model to predict the unknown sample X, and the α-cut set of the obtained prediction output is expressed as:

其中： in:

R_j表示未知样本对应的第j个隐含层节点的输入；R _j represents the input of the jth hidden layer node corresponding to the unknown sample;

r_j1表示未知样本对应的第j个隐含层节点输入的左端点；r _j1 represents the left endpoint of the jth hidden layer node input corresponding to the unknown sample;

r_j2表示未知样本对应的第j个隐含层节点输入的中值点；r _j2 represents the median point of the input of the jth hidden layer node corresponding to the unknown sample;

r_j3表示未知样本对应的第j个隐含层节点输入的右端点；r _j3 represents the right endpoint of the jth hidden layer node input corresponding to the unknown sample;

x_i1表示未知样本的左端点；x _i1 represents the left endpoint of the unknown sample;

x_i2表示未知样本的中值点；x _i2 represents the median point of the unknown sample;

x_i3表示未知样本的右端点。x _i3 represents the right endpoint of the unknown sample.

进一步地，所述方法还包括：Further, the method also includes:

步骤5：通过如下方式对所述得到的预测输出的α‐截集进行修正：Step 5: Correct the α-cut set of the predicted output obtained as follows:

${[[T T]]}_{α α}^{L L} = = min min {{{Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{L L} {β β}_{j j},, {Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{U u} {β β}_{j j}}};; {[[T T]]}_{α α}^{U u} = = max max {{{Σ Σ}_{j j = = 11}^{K K} {[[H h]]}_{α α}^{L L} {β β}_{j j},, {Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{U u} {β β}_{j j}}} . .$

进一步地， further,

一种基于随机权网络的FNR分析模型的训练系统，包括：A training system for FNR analysis model based on random weight network, comprising:

损失函数确定模块，其用于确定用以引导随机权网络隐含层输出权重的训练模式的损失函数E；A loss function determination module, which is used to determine the loss function E of the training mode used to guide the hidden layer output weight of the random weight network;

其中： in:

N为训练样本数目；N is the number of training samples;

α表示截点值；α represents the cutoff value;

其中： in:

训练样本预测输出确定模块，其用于确定所述训练样本X_n预测输出的α-截集的具体形式为：；其中：A training sample prediction output determination module, which is used to determine the specific form of the α-cut set of the training sample X _n prediction output is: ;in:

随机权网络输出层权重确定模块，其用于根据所述损失函数E确定随机权网络输出层权重β的具体形式：Random weight network output layer weight determination module, which is used to determine the specific form of random weight network output layer weight β according to the loss function E:

其中： in:

N×K表示矩阵的阶数为N行K列；N×K means that the order of the matrix is N rows and K columns;

T表示向量的转置；T represents the transpose of the vector;

所述随机权网络输出层权重确定模块根据推导出其中：The random weight network output layer weight determination module is based on Deduced in:

其中：in:

β＝H⁺γ；β = H ⁺ γ;

其中： in:

进一步地，假设未知样本为：Further, suppose the unknown sample is:

X为未知样本；X is an unknown sample;

所述系统还包括：The system also includes:

预测模块，其利用训练得到的FNR分析模型对未知样本X进行预测，得到的预测输出的α‐截集表示为：The prediction module uses the trained FNR analysis model to predict the unknown sample X, and the α-cut set of the obtained prediction output is expressed as:

其中： in:

进一步地，所述训练系统还包括：Further, the training system also includes:

预测输出修正模块，其用于通过如下方式对所述得到的预测输出的α‐截集进行修正：A prediction output modification module, which is used to modify the α-cut set of the obtained prediction output in the following manner:

${[[T T]]}_{α α}^{L L} = = m m i i n no {{{Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{L L} {β β}_{j j},, {Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{U u} {β β}_{j j}}};; {[[T T]]}_{α α}^{U u} = = m m a a x x {{{Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{L L} {β β}_{j j} {Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{U u} {β β}_{j j}}} . .$

进一步地， further,

本发明提供的基于随机权网络的FNR分析模型的训练方法及训练系统中使用的随机权网络不需要迭代训练，它的输入权重随机选取，输出权重基于模糊输入-模糊输出的训练集解析式地求得，并通过对输出层权重解析表达式的正则化处理来控制模型的过拟合。与传统的基于Sigmoid神经网络的FNR模型和基于径向基函数网络的FNR模型相比较，本发明的优势体现在：具有极快的训练速度(最快比现有方法快将近1000倍)和高效的过拟合控制能力(基本上不存在过拟合现象)。The random weight network used in the training method and the training system of the FNR analysis model based on the random weight network provided by the present invention does not need iterative training, its input weight is randomly selected, and the output weight is based on the training set of fuzzy input-fuzzy output. Obtained, and control the overfitting of the model by regularizing the analytical expression of the weight of the output layer. Compared with the traditional FNR model based on Sigmoid neural network and the FNR model based on radial basis function network, the advantages of the present invention are as follows: extremely fast training speed (nearly 1000 times faster than existing methods) and efficient Over-fitting control ability (basically no over-fitting phenomenon).

附图说明Description of drawings

图1：用以处理非线性模糊输入-模糊输出回归问题的随机权网络示意图；Figure 1: Schematic diagram of the random weight network used to deal with the nonlinear fuzzy input-fuzzy output regression problem;

图2：本发明提供的基于随机权网络的FNR分析模型的训练方法的流程示意图；Fig. 2: the schematic flow chart of the training method of the FNR analysis model based on random weight network provided by the present invention;

图3：基于随机权网络的FNR分析模型的训练系统的组成结构示意图。Figure 3: Schematic diagram of the composition and structure of the training system of the FNR analysis model based on the random weight network.

具体实施方式detailed description

为了使本发明的目的、技术方案及优点更加清楚明白，以下结合附图及实施例，对本发明进行进一步详细说明。In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

本发明提供的基于随机权网络的FNR分析模型的训练方法说明如下：The training method of the FNR analysis model based on the random weight network provided by the present invention is described as follows:

设计一个如图1所示的随机权网络RWN(Random Weights Network，随机权网络)，该随机权网络的输入和输出均为三角模糊函数。假设训练集中的第n个训练样本为X_n＝(X_n1,X_n2,…,X_nD)，其对应的实际输出为γ_n，其中X_ni＝(x_ni1，x_ni2，x_ni3)(i＝1,2,…,D)和γ_n＝(y_n1，y_n2，y_n3)均为三角模糊数，[X_ni]_α表示三角模糊数X_ni的α‐截集(α∈(0,1])，D为数据集输入属性的个数，K为随机权网络RWN隐含层节点的个数，w_ji为连接第i个输入层节点和第j个隐含层节点的权重，b_j为第j个隐含层节点的偏置，β_j为第j个隐含层节点与输出层节点链接的权重。w_ji和b_j随机选取，如何确定β_j非迭代式的解析表达式是本发明需要解决的关键核心问题。Design a random weight network RWN (Random Weights Network, random weight network) as shown in Figure 1, the input and output of the random weight network are triangular fuzzy functions. Assume that the nth training sample in the training set is X _n = (X _n1 , X _n2 ,..., X _nD ), and its corresponding actual output is γ _n , where X _ni = (x _ni1 , x _ni2 , x _ni3 )( i=1,2,…,D) and γ _n =(y _n1 , y _n2 , y _n3 ) are both triangular fuzzy numbers, [X _ni ] _α represents the α-cut set of triangular fuzzy numbers X _ni (α∈( 0,1]), D is the number of input attributes of the data set, K is the number of hidden layer nodes of the random weight network RWN, w _ji is the weight connecting the i-th input layer node and the j-th hidden layer node , b _j is the bias of the jth hidden layer node, β _j is the weight of the link between the jth hidden layer node and the output layer node. w _ji and b _j are randomly selected, how to determine the non-iterative analysis of β _j Expression is the key core problem that the present invention needs to solve.

为确定图1所示的随机权网络RWN中的输出层权重β_j，本发明提供了一种基于随机权网络的FNR分析模型的训练方法，如图2所示，该训练方法包括如下步骤：For determining the output layer weight β _j in the random weight network RWN shown in Figure 1, the present invention provides a kind of training method based on the FNR analysis model of random weight network, as shown in Figure 2, this training method comprises the following steps:

步骤S1：确定用以引导随机权网络隐含层输出权重的训练模式的损失函数E。Step S1: Determine the loss function E of the training mode used to guide the output weight of the hidden layer of the random weight network.

其中： in:

N为训练样本数目；N is the number of training samples;

α表示截点值；α represents the cutoff value;

其中： in:

表示训练样本X_n实际输出的α-截集的上边界点。 Indicates the upper boundary point of the α-cut set actually output by the training sample X _n .

步骤S2：确定所述训练样本X_n预测输出的α-截集的具体形式为，其中：Step S2: Determine the specific form of the α-cut set of the predicted output of the training sample X _n as ,in:

β_j表示第j个隐含层节点与输出层节点链接的权重。β _j represents the weight of the link between the jth hidden layer node and the output layer node.

步骤S3：根据所述损失函数E确定随机权网络输出层权重β的具体形式。具体为：Step S3: Determine the specific form of the output layer weight β of the random weight network according to the loss function E. Specifically:

其中： in:

T表示向量的转置。T represents the transpose of a vector.

根据推导出according to Deduced

其中： in:

其中：in:

y_N3表示第N个训练样本实际输出的α‐截集的右端点。y _N3 represents the right endpoint of the α-cut set actually output by the Nth training sample.

β＝H⁺γ。β = H ⁺ γ.

本实施例中，假设训练样本X_n对应的隐含层输入向量为R_n＝(R_n1,R_n2,…,R_nK)，则第n个训练样本对应的第j个隐含层节点的输入R_nj对应的三角模糊数为：In this embodiment, assuming that the hidden layer input vector corresponding to the training sample X _n is R _n = (R _n1 , R _n2 ,..., R _nK ), then the jth hidden layer node corresponding to the nth training sample is The triangular fuzzy number corresponding to input R _nj is:

其中： in:

利用H_n＝(H_n1,H_n2,…,H_nK)表示训练样本X_n对应的隐含层输出向量，则分量H_nj表示为：Use H _n =(H _n1 ,H _n2 ,…,H _nK ) to represent the hidden layer output vector corresponding to the training sample X _n , then the component H _nj is expressed as:

本实施例中，假设未知样本为X＝(X₁,X₂,…,X_D)＝((x₁₁，x₁₂，x₁₃),(x₂₁，x₂₂，x₂₃),…,(x_D1，x_D2，x_D3))，其中：In this embodiment, it is assumed that the unknown samples are X=(X ₁ ,X ₂ ,…,X _D )=((x ₁₁ ,x ₁₂ ,x ₁₃ ),(x ₂₁ ,x ₂₂ ,x ₂₃ ),…,( x _D1 , x _D2 , x _D3 )), where:

X为未知样本；X is an unknown sample;

则所述方法还包括：Then described method also comprises:

步骤S4：利用训练得到的FNR分析模型对未知样本X进行预测，得到的预测输出的α‐截集表示为其中：Step S4: Use the trained FNR analysis model to predict the unknown sample X, and the α-cut set of the obtained prediction output is expressed as in:

其中： in:

本实施例中，所述方法还包括：In this embodiment, the method also includes:

步骤S5：通过如下方式对所述得到的预测输出的α‐截集进行修正：Step S5: Correct the α-cut set of the predicted output obtained in the following way:

${[[T T]]}_{α α}^{L L} = = min min {{{Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{L L} {β β}_{j j},, {Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{U u} {β β}_{j j}}};; {[[T T]]}_{α α}^{U u} = = max max {{{Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{L L} {β β}_{j j},, {Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{U u} {β β}_{j j}}} . .$

本实施例中， In this example,

如图3所示，本发明还提供了一种基于随机权网络的FNR分析模型的训练系统，包括损失函数确定模块1、训练样本预测输出确定模块2和随机权网络输出层权重确定模块3。As shown in Figure 3, the present invention also provides a training system based on the FNR analysis model of the random weight network, including a loss function determination module 1, a training sample prediction output determination module 2 and a random weight network output layer weight determination module 3.

损失函数确定模块1用于确定用以引导随机权网络隐含层输出权重的训练模式的损失函数E。损失函数E的表达式如下：The loss function determination module 1 is used to determine the loss function E of the training mode used to guide the output weight of the hidden layer of the random weight network. The expression of the loss function E is as follows:

其中： in:

N为训练样本数目；N is the number of training samples;

α表示截点值；α represents the cutoff value;

其中： in:

训练样本预测输出确定模块2用于确定所述训练样本X_n预测输出的α-截集的具体形式为：。其中：The specific form of the α-cut set that the training sample prediction output determination module 2 is used to determine the prediction output of the training sample X _n is: . in:

随机权网络输出层权重确定模块3用于根据所述损失函数E确定随机权网络输出层权重β的具体形式：The random weight network output layer weight determination module 3 is used to determine the specific form of the random weight network output layer weight β according to the loss function E:

其中： in:

T表示向量的转置。T represents the transpose of a vector.

所述随机权网络输出层权重确定模块3根据推导出其中：The random weight network output layer weight determination module 3 is based on Deduced in:

其中：in:

β＝H⁺γ；β = H ⁺ γ;

其中： in:

x_ni3表示第n个训练样本的右端点。x _ni3 represents the right endpoint of the nth training sample.

本实施例中，假设未知样本为X＝(X₁,X₂,…,X_D)＝((x₁₁，x₁₂，x₁₃),(x₂₁，x₂₂，x₂₃),…,(x_D1，x_D2，x_D3))。其中：In this embodiment, it is assumed that the unknown samples are X=(X ₁ ,X ₂ ,…,X _D )=((x ₁₁ ,x ₁₂ ,x ₁₃ ),(x ₂₁ ,x ₂₂ ,x ₂₃ ),…,( x _D1 , x _D2 , x _D3 )). in:

X为未知样本；X is an unknown sample;

x_D3表示三角模糊数X_D的右端点。则所述系统还包括预测模块4，预测模块4利用训练得到的FNR分析模型对未知样本X进行预测，得到的预测输出的α‐截集表示为：x _D3 represents the right endpoint of the triangular fuzzy number X _D . Then the system also includes a prediction module 4, the prediction module 4 uses the FNR analysis model obtained by training to predict the unknown sample X, and the α-cut set of the obtained prediction output is expressed as:

其中： in:

本实施例中，所述训练系统还包括预测输出修正模块5，预测输出修正模块5用于通过如下方式对所述得到的预测输出的α‐截集进行修正：In this embodiment, the training system also includes a prediction output correction module 5, and the prediction output correction module 5 is used to correct the α-cut set of the obtained prediction output in the following manner:

本实施例中， In this example,

以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内所作的任何修改、等同替换和改进等，均应包含在本发明的保护范围之内。The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present invention should be included in the protection of the present invention. within range.

Claims

1. a training method based on the FNR analysis model of random weight network, is characterized in that, comprises the steps:

Step 1: Determine the loss function E of the training mode used to guide the output weight of the hidden layer of the random weight network;

The expression of the loss function E is as follows:

in:

N is the number of training samples;

α represents the cutoff value;

[T _n ] _α is the α-cut set of the predicted output of the training sample X _n ,

is the α-cut set actually output by the training sample X _n ,

in:

Represents the lower boundary point of the α-cut set of the training sample X _n predicted output;

Represents the upper boundary point of the α-cut set of the training sample X _n predicted output;

Represents the lower boundary point of the α-cut set actually output by the training sample X _n ;

Represents the upper boundary point of the α-cut set actually output by the training sample X _n ;

Step 2: Determine the specific form of the α-cut set of the predicted output of the training sample X _n as:

;in:

H _nj represents the output of the jth hidden layer node corresponding to the nth training sample;

Represents the lower boundary point of the α-cut set of H _nj ;

Represents the upper boundary point of the α-cut set of H _nj ;

r _nj1 represents the left endpoint of the jth hidden layer node input corresponding to the nth training sample;

r _nj2 represents the median point of the jth hidden layer node input corresponding to the nth training sample;

r _nj3 represents the right endpoint of the jth hidden layer node input corresponding to the nth training sample;

β _j represents the weight of the link between the jth hidden layer node and the output layer node;

Step 3: Determine the specific form of the output layer weight β of the random weight network according to the loss function E; specifically:

in:

is the lower boundary matrix of the α-cut set output by the hidden layer of the random weight network,

is the upper boundary matrix of the α-cut set output by the hidden layer of the random weight network,

is the lower boundary vector of the actual output α-cut set,

is the upper boundary vector of the actual output α-cut set, in:

_N×K means that the order of the matrix is N rows and K columns;

_T represents the transpose of the vector;

according to Deduced

in:

is the integral of the lower bound matrix of the α-cut set output by the hidden layer,

is the integral of the upper bound matrix of the α-cut set output by the hidden layer,

is the integral of the lower boundary vector of the α-cut set of the actual output,

is the integral of the upper boundary vector of the α-cut set of the actual output,

in:

y _N1 represents the left endpoint of the α-cut set actually output by the Nth training sample;

y _N2 represents the median point of the α-cut set actually output by the Nth training sample;

y _N3 represents the right endpoint of the α-cut set actually output by the Nth training sample;

make Then the analytical expression of the weight β of the output layer of the random weight network is obtained as:

in, is the generalized inverse matrix of matrix H,

Among them, C is a regularization factor, which is used to control the overfitting of the random weight network, C>0; I is the identity matrix.

2. The training method according to claim 1, wherein, assuming that the hidden layer input vector corresponding to the training sample X _n is R _n = (R _n1 , R _n2 ,..., R _nK ), then the nth training The triangular fuzzy number corresponding to the input R _nj of the jth hidden layer node corresponding to the sample is:

in:

w _ji represents the weight of the connection between the i-th input layer node and the j-th hidden layer node of the fuzzy random weight network;

x _ni1 represents the left endpoint of the nth training sample;

x _ni2 represents the median point of the nth training sample;

x _ni3 represents the right endpoint of the nth training sample;

Use H _n =(H _n1 ,H _n2 ,…,H _nK ) to represent the hidden layer output vector corresponding to the training sample X _n , then the component H _nj is expressed as:

{H h}_{n no j j} = = (({h h}_{n no j j 11},, {h h}_{n no j j 22},, {h h}_{n no j j 33})) = = ((\frac{11}{11 + + exp exp ((- - {r r}_{n no j j 11}))},, \frac{11}{11 + + exp exp ((- - {r r}_{n no j j 22}))},, \frac{11}{11 + + exp exp ((- - {r r}_{n no j j 33}))})) . .

3. training method as claimed in claim 1, is characterized in that, suppose unknown sample is:

X=(X ₁ ,X ₂ ,...,X _D )=((x ₁₁ ,x ₁₂ ,x ₁₃ ),(x ₂₁ ,x ₂₂ ,x ₂₃ ),...,(x _D1 ,x _D2 ,x _D3 ) );in:

X is an unknown sample;

X _D represents the Dth triangular fuzzy number attribute of the unknown sample;

x _D1 represents the left endpoint of the triangular fuzzy number X _D ;

x _D2 represents the median point of the triangular fuzzy number X _D ;

x _D3 represents the right endpoint of the triangular fuzzy number X _D ;

The method also includes:

Step 4: Use the trained FNR analysis model to predict the unknown sample X, and the α-cut set of the obtained prediction output is expressed as:

in:

[[{[[{H h}_{j j}]]}_{α α}^{L L},, {[[{H h}_{j j}]]}_{α α}^{U u}]] = = [[\frac{11}{11 + + exp exp [[- - [[{αr αr}_{j j 22} + + ((11 - - α α)) {r r}_{j j 11}]]]]},, \frac{11}{11 + + exp exp [[- - [[{αr αr}_{j j 22} + + ((11 - - α α)) {r r}_{j j 33}]]]]}]],,

in:

R _j represents the input of the jth hidden layer node corresponding to the unknown sample;

r _j1 represents the left endpoint of the jth hidden layer node input corresponding to the unknown sample;

r _j2 represents the median point of the input of the jth hidden layer node corresponding to the unknown sample;

r _j3 represents the right endpoint of the jth hidden layer node input corresponding to the unknown sample;

x _i1 represents the left endpoint of the unknown sample;

x _i2 represents the median point of the unknown sample;

x _i3 represents the right endpoint of the unknown sample.

4. training method as claimed in claim 3, is characterized in that, described method also comprises:

Step 5: Correct the α-cut set of the predicted output obtained as follows:

{[[T T]]}_{α α}^{L L} = = min min {{{Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{L L} {β β}_{j j},, {Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{U u} {β β}_{j j}}};; {[[T T]]}_{α α}^{U u} = = max max {{{Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{L L} {β β}_{j j},, {Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{U u} {β β}_{j j}}} . .

5. training method as claimed in claim 1, is characterized in that:

{&Integral; &Integral;}_{00}^{11} (({H h}_{α α}^{L L} + + {H h}_{α α}^{U u})) d d α α = = {((22 + + \frac{I I n no \frac{11 + + exp exp ((- - {r r}_{n no j j 22}))}{11 + + exp exp ((- - {r r}_{n no j j 11}))}}{{r r}_{n no j j 22} - - {r r}_{n no j j 11}} + + \frac{I I n no \frac{11 + + exp exp ((- - {r r}_{n no j j 22}))}{11 + + exp exp ((- - {r r}_{n no j j 33}))}}{{r r}_{n no j j 22} - - {r r}_{n no j j 33}}))}_{N N \times \times K K};;

6. a kind of training system based on the FNR analysis model of random weight network, it is characterized in that, comprising:

A loss function determination module, which is used to determine the loss function E of the training mode used to guide the hidden layer output weight of the random weight network;

The expression of the loss function E is as follows:

in:

N is the number of training samples;

α represents the cutoff value;

is the α-cut set actually output by the training sample X _n ,

in:

A training sample prediction output determination module, which is used to determine the specific form of the α-cut set of the training sample X _n prediction output is: ;in:

Represents the lower boundary point of the α-cut set of H _nj ;

Represents the upper boundary point of the α-cut set of H _nj ;

Random weight network output layer weight determination module, which is used to determine the specific form of random weight network output layer weight β according to the loss function E:

in:

is the lower boundary vector of the actual output α-cut set,

is the upper boundary vector of the actual output α-cut set, in:

_N×K means that the order of the matrix is N rows and K columns;

_T represents the transpose of the vector;

The random weight network output layer weight determination module is based on Deduced in:

in:

in, is the generalized inverse matrix of matrix H,

7. The training system according to claim 6, wherein, assuming that the hidden layer input vector corresponding to the training sample X _n is R _n = (R _n1 , R _n2 ,..., R _nK ), the nth training The triangular fuzzy number corresponding to the input R _nj of the jth hidden layer node corresponding to the sample is:

in:

x _ni1 represents the left endpoint of the nth training sample;

x _ni2 represents the median point of the nth training sample;

x _ni3 represents the right endpoint of the nth training sample;

{H h}_{n no j j} = = (({h h}_{n no j j 11},, {h h}_{n no j j 22},, {h h}_{n no j j 33})) = = ((\frac{11}{11 + + exp exp ((- - {r r}_{n no j j 11}))},, \frac{11}{11 + + exp exp ((- - {r r}_{n no j j 22}))},, \frac{11}{11 + + exp exp ((- - {r r}_{n no j j 33}))})) . .

8. training system as claimed in claim 6, is characterized in that, assumes that unknown sample is:

X is an unknown sample;

x _D1 represents the left endpoint of the triangular fuzzy number X _D ;

x _D2 represents the median point of the triangular fuzzy number X _D ;

x _D3 represents the right endpoint of the triangular fuzzy number X _D ;

The system also includes:

The prediction module uses the trained FNR analysis model to predict the unknown sample X, and the α-cut set of the obtained prediction output is expressed as:

in:

[[{[[{H h}_{j j}]]}_{α α}^{L L},, {[[{H h}_{j j}]]}_{α α}^{U u}]] = = [[\frac{11}{11 + + exp exp [[- - [[{αr αr}_{j j 22} + + ((11 - - α α)) {r r}_{j j 11}]]]]},, \frac{11}{11 + + exp exp [[- - [[{αr αr}_{j j 22} + + ((11 - - α α)) {r r}_{j j 33}]]]]}]],,

in:

x _i1 represents the left endpoint of the unknown sample;

x _i2 represents the median point of the unknown sample;

x _i3 represents the right endpoint of the unknown sample.

9. training system as claimed in claim 6, is characterized in that, described training system also comprises:

A prediction output modification module, which is used to modify the α-cut set of the obtained prediction output in the following manner:

{[[T T]]}_{α α}^{L L} = = min min {{{Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{L L} {β β}_{j j},, {Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{U u} {β β}_{j j}}};; {[[T T]]}_{α α}^{U u} = = max max {{{Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{L L} {β β}_{j j},, {Σ Σ}_{j j = = 11}^{K K} {[[{H h}_{j j}]]}_{α α}^{U u} {β β}_{j j}}} . .

10. The training system of claim 6, wherein:

{&Integral; &Integral;}_{00}^{11} (({H h}_{α α}^{L L} + + {H h}_{α α}^{U u})) d d α α = = {((22 + + \frac{I I n no \frac{11 + + exp exp ((- - {r r}_{n no j j 22}))}{11 + + exp exp ((- - {r r}_{n no j j 11}))}}{{r r}_{n no j j 22} - - {r r}_{n no j j 11}} + + \frac{I I n no \frac{11 + + exp exp ((- - {r r}_{n no j j 22}))}{11 + + exp exp ((- - {r r}_{n no j j 33}))}}{{r r}_{n no j j 22} - - {r r}_{n no j j 33}}))}_{N N \times \times K K};;