Analysis of 43 cases of MATLAB neural network: Chapter 29 research on the application of limit learning machine in regression fitting and classification -- Comparative Experiment

1. Preface

《MATLAB neural network 43 A case study 》 yes MATLAB Technology Forum （www.matlabsky.com） planning , Led by teacher wangxiaochuan ,2013 Beijing University of Aeronautics and Astronautics Press MATLAB A book for tools MATLAB Example teaching books , Is in 《MATLAB neural network 30 A case study 》 On the basis of modification 、 Complementary , Adhering to “ Theoretical explanation — case analysis — Application extension ” This feature , Help readers to be more intuitive 、 Learn neural networks vividly .

《MATLAB neural network 43 A case study 》 share 43 Chapter , The content covers common neural networks （BP、RBF、SOM、Hopfield、Elman、LVQ、Kohonen、GRNN、NARX etc. ） And related intelligent algorithms （SVM、 Decision tree 、 Random forests 、 Extreme learning machine, etc ）. meanwhile , Some chapters also cover common optimization algorithms （ Genetic algorithm (ga) 、 Ant colony algorithm, etc ） And neural network . Besides ,《MATLAB neural network 43 A case study 》 It also introduces MATLAB R2012b New functions and features of neural network toolbox in , Such as neural network parallel computing 、 Custom neural networks 、 Efficient programming of neural network, etc .

In recent years, with the rise of artificial intelligence research , The related direction of neural network has also ushered in another upsurge of research , Because of its outstanding performance in the field of signal processing , The neural network method is also being applied to various applications in the direction of speech and image , This paper combines the cases in the book , It is simulated and realized , It's a relearning , I hope I can review the old and know the new , Strengthen and improve my understanding and practice of the application of neural network in various fields . I just started this book on catching more fish , Let's start the simulation example , Mainly to introduce the source code application examples in each chapter , This paper is mainly based on MATLAB2015b(32 position ) Platform simulation implementation , This is an example of the application of extreme learning machine in regression fitting and classification in Chapter 29 of this book , Don't talk much , Start ！

2. MATLAB Simulation example 1

open MATLAB, Click on “ Home page ”, Click on “ open ”, Find the sample file

Choose main.m, Click on “ open ”

main.m Source code is as follows ：

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% function ： Research on the application of limit learning machine in classification problem 
% Environmental Science ：Win7,Matlab2015b
%Modi: C.S
% Time ：2022-06-20
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%  Research on the application of limit learning machine in classification problem 

%%  Clear environment variables 
clear all
clc
warning off
tic
%%  Import data 
load data.mat
%  Randomly generated training set / Test set 
a = randperm(569);
Train = data(a(1:500),:);
Test = data(a(501:end),:);
%  Training data 
P_train = Train(:,3:end)';
T_train = Train(:,2)';
%  Test data 
P_test = Test(:,3:end)';
T_test = Test(:,2)';

tic

%% ELM establish / Training 
[IW,B,LW,TF,TYPE] = elmtrain(P_train,T_train,100,'sig',1);

%% ELM The simulation test 
T_sim_1 = elmpredict(P_train,IW,B,LW,TF,TYPE);
T_sim_2 = elmpredict(P_test,IW,B,LW,TF,TYPE);

toc

%%  Results contrast 
result_1 = [T_train' T_sim_1'];
result_2 = [T_test' T_sim_2'];
%  Training set accuracy 
k1 = length(find(T_train == T_sim_1));
n1 = length(T_train);
Accuracy_1 = k1 / n1 * 100;
disp([' Training set accuracy Accuracy = ' num2str(Accuracy_1) '%(' num2str(k1) '/' num2str(n1) ')'])
%  Test set accuracy 
k2 = length(find(T_test == T_sim_2));
n2 = length(T_test);
Accuracy_2 = k2 / n2 * 100;
disp([' Test set accuracy Accuracy = ' num2str(Accuracy_2) '%(' num2str(k2) '/' num2str(n2) ')'])

%%  Show 
count_B = length(find(T_train == 1));
count_M = length(find(T_train == 2));
rate_B = count_B / 500;
rate_M = count_M / 500;
total_B = length(find(data(:,2) == 1));
total_M = length(find(data(:,2) == 2));
number_B = length(find(T_test == 1));
number_M = length(find(T_test == 2));
number_B_sim = length(find(T_sim_2 == 1 & T_test == 1));
number_M_sim = length(find(T_sim_2 == 2 & T_test == 2));
disp([' Total number of cases ：' num2str(569)...
      '  Benign ：' num2str(total_B)...
      '  Malignant ：' num2str(total_M)]);
disp([' Total number of training set cases ：' num2str(500)...
      '  Benign ：' num2str(count_B)...
      '  Malignant ：' num2str(count_M)]);
disp([' Total number of cases in the test set ：' num2str(69)...
      '  Benign ：' num2str(number_B)...
      '  Malignant ：' num2str(number_M)]);
disp([' Benign breast tumor was diagnosed ：' num2str(number_B_sim)...
      '  Misdiagnosis ：' num2str(number_B - number_B_sim)...
      '  Diagnostic rate p1=' num2str(number_B_sim/number_B*100) '%']);
disp([' Malignant breast tumor was diagnosed ：' num2str(number_M_sim)...
      '  Misdiagnosis ：' num2str(number_M - number_M_sim)...
      '  Diagnostic rate p2=' num2str(number_M_sim/number_M*100) '%']);
  
  
R = [];
for i = 50:50:500
    %% ELM establish / Training 
    [IW,B,LW,TF,TYPE] = elmtrain(P_train,T_train,i,'sig',1);
    
    %% ELM The simulation test 
    T_sim_1 = elmpredict(P_train,IW,B,LW,TF,TYPE);
    T_sim_2 = elmpredict(P_test,IW,B,LW,TF,TYPE);
    
    %%  Results contrast 
    result_1 = [T_train' T_sim_1'];
    result_2 = [T_test' T_sim_2'];
    %  Training set accuracy 
    k1 = length(find(T_train == T_sim_1));
    n1 = length(T_train);
    Accuracy_1 = k1 / n1 * 100;
%     disp([' Training set accuracy Accuracy = ' num2str(Accuracy_1) '%(' num2str(k1) '/' num2str(n1) ')'])
    %  Test set accuracy 
    k2 = length(find(T_test == T_sim_2));
    n2 = length(T_test);
    Accuracy_2 = k2 / n2 * 100;
%     disp([' Test set accuracy Accuracy = ' num2str(Accuracy_2) '%(' num2str(k2) '/' num2str(n2) ')'])
    R = [R;Accuracy_1 Accuracy_2];
end
  
figure
plot(50:50:500,R(:,2),'b:o')
xlabel(' Number of neurons in the hidden layer ')
ylabel(' Test set prediction accuracy （%）')
title(' Number of neurons in the hidden layer ELM The impact of performance ')
toc

Add completed , Click on “ function ”, Start emulating , The output simulation results are as follows ：

 Time has passed  0.138923  second .
 Training set accuracy Accuracy = 87%(435/500)
 Test set accuracy Accuracy = 88.4058%(61/69)
 Total number of cases ：569   Benign ：357   Malignant ：212
 Total number of training set cases ：500   Benign ：314   Malignant ：186
 Total number of cases in the test set ：69   Benign ：43   Malignant ：26
 Benign breast tumor was diagnosed ：40   Misdiagnosis ：3   Diagnostic rate p1=93.0233%
 Malignant breast tumor was diagnosed ：21   Misdiagnosis ：5   Diagnostic rate p2=80.7692%
 Time has passed  0.704174  second .

3. MATLAB Simulation example 2

open MATLAB, Click on “ Home page ”, Click on “ open ”, Find the sample file

Choose main.m, Click on “ open ”

main.m Source code is as follows ：

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% function ： Research on the application of limit learning machine in regression fitting problem 
% Environmental Science ：Win7,Matlab2015b
%Modi: C.S
% Time ：2022-06-20
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%  Research on the application of limit learning machine in regression fitting problem 

%%  Clear environment variables 
clear all
clc
tic
%%  Import data 
load data
%  Randomly generate training sets 、 Test set 
k = randperm(size(input,1));
%  Training set ——1900 Samples 
P_train=input(k(1:1900),:)';
T_train=output(k(1:1900));
%  Test set ——100 Samples 
P_test=input(k(1901:2000),:)';
T_test=output(k(1901:2000));

%%  normalization 
%  Training set 
[Pn_train,inputps] = mapminmax(P_train,-1,1);
Pn_test = mapminmax('apply',P_test,inputps);
%  Test set 
[Tn_train,outputps] = mapminmax(T_train,-1,1);
Tn_test = mapminmax('apply',T_test,outputps);

tic
%% ELM establish / Training 
[IW,B,LW,TF,TYPE] = elmtrain(Pn_train,Tn_train,20,'sig',0);

%% ELM The simulation test 
Tn_sim = elmpredict(Pn_test,IW,B,LW,TF,TYPE);
%  Anti normalization 
T_sim = mapminmax('reverse',Tn_sim,outputps);

toc
%%  Results contrast 
result = [T_test' T_sim'];
%  Mean square error 
E = mse(T_sim - T_test)
%  Coefficient of determination 
N = length(T_test);
R2 = (N*sum(T_sim.*T_test)-sum(T_sim)*sum(T_test))^2/((N*sum((T_sim).^2)-(sum(T_sim))^2)*(N*sum((T_test).^2)-(sum(T_test))^2))

%%  mapping 
figure
plot(1:length(T_test),T_test,'r*')
hold on
plot(1:length(T_sim),T_sim,'b:o')
xlabel(' Test set sample number ')
ylabel(' Test set output ')
title('ELM Test set output ')
legend(' Expected output ',' Forecast output ')

figure
plot(1:length(T_test),T_test-T_sim,'r-*')
xlabel(' Test set sample number ')
ylabel(' Absolute error ')
title('ELM Test set prediction error ')
toc

Add completed , Click on “ function ”, Start emulating , The output simulation results are as follows ：

 Time has passed  0.026963  second .

E =

    0.0012


R2 =

    1.0000

 Time has passed  0.960279  second .

4. Summary

Extreme learning machine （Extreme Learning Machine, ELM） or “ Transfinite learning machine ” It is a kind of neural network based on feedforward （Feedforward Neuron Network, FNN） Constructed machine learning system or method , It is applicable to supervised learning and unsupervised learning .ELM It is regarded as a special kind of FNN, Or right FNN And the improvement of its back propagation algorithm , Its characteristic is that the weights of hidden layer nodes are given randomly or artificially , And no update is required , The learning process only calculates the output weights . Conventional ELM With single hidden layer , In conjunction with other shallow learning systems , For example, a single-layer perceptron （single layer perceptron） And support vector machines （Support Vector Machine, SVM） In comparison with time , It is considered that it may have advantages in learning speed and generalization ability .ELM Some of the improved versions of the have achieved depth structure by introducing self encoder to construct or stack hidden layers , Be able to conduct representational learning .ELM Applications include computer vision and bioinformatics , It is also applied to some earth sciences 、 Regression in environmental science .
Interested in the content of this chapter or want to fully learn and understand , It is suggested to study the contents of chapter 29 in the book . Some of these knowledge points will be supplemented on the basis of their own understanding in the later stage , Welcome to study and exchange together .