Analysis of 43 cases of MATLAB neural network: Chapter 10 classification of discrete Hopfield Neural Network -- evaluation of scientific research ability of colleges and Universities

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 the tenth chapter of the book Hopfield Examples of neural network classification , Don't talk much , Start ！

2. MATLAB Simulation example

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

Choose chapter10.m, Click on “ open ”

chapter10.m Source code is as follows ：

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% function ： discrete Hopfield The classification of —— Evaluation of scientific research ability in Colleges and Universities 
% Environmental Science ：Win7,Matlab2015b
%Modi: C.S
% Time ：2022-06-09
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%  Clear environment variables 
clear all
clc
tic
%%  Import data 
load class.mat

%%  The target vector 
T = [class_1 class_2 class_3 class_4 class_5];

%%  Creating networks 
net = newhop(T);

%%  Import samples to be classified 
load sim.mat
A = {
    [sim_1 sim_2 sim_3 sim_4 sim_5]};

%%  Network simulation 
Y = sim(net,{
    25 20},{
    },A);

%%  Results show 
Y1 = Y{
    20}(:,1:5);
Y2 = Y{
    20}(:,6:10);
Y3 = Y{
    20}(:,11:15);
Y4 = Y{
    20}(:,16:20);
Y5 = Y{
    20}(:,21:25);

%%  mapping 
result = {
    T;A{
    1};Y{
    20}};
figure
for p = 1:3
    for k = 1:5 
        subplot(3,5,(p-1)*5+k)
        temp = result{
    p}(:,(k-1)*5+1:k*5);
        [m,n] = size(temp);
        for i = 1:m
            for j = 1:n
                if temp(i,j) > 0
                   plot(j,m-i,'ko','MarkerFaceColor','k');
                else
                   plot(j,m-i,'ko');
                end
                hold on
            end
        end
        axis([0 6 0 12])
        axis off
        if p == 1
           title(['class' num2str(k)])
        elseif p == 2
           title(['pre-sim' num2str(k)])
        else
           title(['sim' num2str(k)])
        end
    end                
end

%  Case expansion ( Unable to distinguish the situation )
noisy = [1 -1 -1 -1 -1;-1 -1 -1 1 -1;
        -1 1 -1 -1 -1;-1 1 -1 -1 -1;
        1 -1 -1 -1 -1;-1 -1 1 -1 -1;
        -1 -1 -1 1 -1;-1 -1 -1 -1 1;
        -1 1 -1 -1 -1;-1 -1 -1 1 -1;
        -1 -1 1 -1 -1];
y = sim(net,{
    5 100},{
    },{
    noisy});
a = y{
    100};
toc

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

3. Summary

Hopfield Neural network is abbreviated as HNN（Hopfiled Neural Network), Is in 1982 By the California Institute of technology J.Hopfield Professor proposed , It is a single-layer feedback neural network .Hopfield Network is a kind of recurrent neural network , Feedback connection from output to input , Each neuron is connected to all other neurons , Also known as full Internet . It guarantees convergence to the local minimum , But it converges to the wrong local minimum （local minimum）, Not the global minimum （global minimum） It can also happen . The last chapter is about the application of discretization Hopfield Neural network is used to recognize digital images , Interested in the content of this chapter or want to fully learn and understand , It is recommended to study the contents of Chapter 10 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 .