《MATLAB 神经网络43个案例分析》：第15章 SVM的参数优化——如何更好的提升分类器的性能

企业开发 2022-06-14 14:19:20 阅读次数: 0

《MATLAB 神经网络43个案例分析》：第15章 SVM的参数优化——如何更好的提升分类器的性能

1. 前言

《MATLAB 神经网络43个案例分析》是MATLAB技术论坛（www.matlabsky.com）策划，由王小川老师主导，2013年北京航空航天大学出版社出版的关于MATLAB为工具的一本MATLAB实例教学书籍，是在《MATLAB神经网络30个案例分析》的基础上修改、补充而成的，秉承着“理论讲解—案例分析—应用扩展”这一特色，帮助读者更加直观、生动地学习神经网络。

《MATLAB神经网络43个案例分析》共有43章，内容涵盖常见的神经网络（BP、RBF、SOM、Hopfield、Elman、LVQ、Kohonen、GRNN、NARX等）以及相关智能算法（SVM、决策树、随机森林、极限学习机等）。同时，部分章节也涉及了常见的优化算法（遗传算法、蚁群算法等）与神经网络的结合问题。此外，《MATLAB神经网络43个案例分析》还介绍了MATLAB R2012b中神经网络工具箱的新增功能与特性，如神经网络并行计算、定制神经网络、神经网络高效编程等。

近年来随着人工智能研究的兴起，神经网络这个相关方向也迎来了又一阵研究热潮，由于其在信号处理领域中的不俗表现，神经网络方法也在不断深入应用到语音和图像方向的各种应用当中，本文结合书中案例，对其进行仿真实现，也算是进行一次重新学习，希望可以温故知新，加强并提升自己对神经网络这一方法在各领域中应用的理解与实践。自己正好在多抓鱼上入手了这本书，下面开始进行仿真示例，主要以介绍各章节中源码应用示例为主，本文主要基于MATLAB2015b(32位)平台仿真实现，这是本书第十五章 SVM的参数优化实例，话不多说，开始！

2. MATLAB 仿真示例一

打开MATLAB，点击“主页”，点击“打开”，找到示例文件
在这里插入图片描述
选中chapter_GA.m，点击“打开”

chapter_GA.m源码如下：

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%功能：SVM的参数优化——如何更好的提升分类器的性能一
%环境：Win7，Matlab2015b
%Modi: C.S
%时间：2022-06-14
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Matlab神经网络43个案例分析

% SVM的参数优化——如何更好的提升分类器的性能
% by 李洋(faruto)
% http://www.matlabsky.com
% Email:faruto@163.com
% http://weibo.com/faruto 
% http://blog.sina.com.cn/faruto
% 2013.01.01
%% 清空环境变量
function chapter_GA
close all;
clear;
clc;
format compact;
%% 数据提取
tic
% 载入测试数据wine,其中包含的数据为classnumber = 3,wine:178*13的矩阵,wine_labes:178*1的列向量
load wine.mat;

% 画出测试数据的box可视化图
figure;
boxplot(wine,'orientation','horizontal','labels',categories);
title('wine数据的box可视化图','FontSize',12);
xlabel('属性值','FontSize',12);
grid on;

% 画出测试数据的分维可视化图
figure
subplot(3,5,1);
hold on
for run = 1:178
    plot(run,wine_labels(run),'*');
end
xlabel('样本','FontSize',10);
ylabel('类别标签','FontSize',10);
title('class','FontSize',10);
for run = 2:14
    subplot(3,5,run);
    hold on;
    str = ['attrib ',num2str(run-1)];
    for i = 1:178
        plot(i,wine(i,run-1),'*');
    end
    xlabel('样本','FontSize',10);
    ylabel('属性值','FontSize',10);
    title(str,'FontSize',10);
end

% 选定训练集和测试集

% 将第一类的1-30,第二类的60-95,第三类的131-153做为训练集
train_wine = [wine(1:30,:);wine(60:95,:);wine(131:153,:)];
% 相应的训练集的标签也要分离出来
train_wine_labels = [wine_labels(1:30);wine_labels(60:95);wine_labels(131:153)];
% 将第一类的31-59,第二类的96-130,第三类的154-178做为测试集
test_wine = [wine(31:59,:);wine(96:130,:);wine(154:178,:)];
% 相应的测试集的标签也要分离出来
test_wine_labels = [wine_labels(31:59);wine_labels(96:130);wine_labels(154:178)];

%% 数据预处理
% 数据预处理,将训练集和测试集归一化到[0,1]区间

[mtrain,ntrain] = size(train_wine);
[mtest,ntest] = size(test_wine);

dataset = [train_wine;test_wine];
% mapminmax为MATLAB自带的归一化函数
[dataset_scale,ps] = mapminmax(dataset',0,1);
dataset_scale = dataset_scale';

train_wine = dataset_scale(1:mtrain,:);
test_wine = dataset_scale( (mtrain+1):(mtrain+mtest),: );
%% 选择GA最佳的SVM参数c&g

% GA的参数选项初始化
ga_option.maxgen = 200;
ga_option.sizepop = 20; 
ga_option.cbound = [0,100];
ga_option.gbound = [0,100];
ga_option.v = 5;
ga_option.ggap = 0.9;

[bestacc,bestc,bestg] = gaSVMcgForClass(train_wine_labels,train_wine,ga_option);

% 打印选择结果
disp('打印选择结果');
str = sprintf( 'Best Cross Validation Accuracy = %g%% Best c = %g Best g = %g',bestacc,bestc,bestg);
disp(str);

%% 利用最佳的参数进行SVM网络训练
cmd = ['-c ',num2str(bestc),' -g ',num2str(bestg)];
model = svmtrain(train_wine_labels,train_wine,cmd);

%% SVM网络预测
[predict_label,accuracy] = svmpredict(test_wine_labels,test_wine,model);

% 打印测试集分类准确率
total = length(test_wine_labels);
right = sum(predict_label == test_wine_labels);
disp('打印测试集分类准确率');
str = sprintf( 'Accuracy = %g%% (%d/%d)',accuracy(1),right,total);
disp(str);

%% 结果分析

% 测试集的实际分类和预测分类图
figure;
hold on;
plot(test_wine_labels,'o');
plot(predict_label,'r*');
xlabel('测试集样本','FontSize',12);
ylabel('类别标签','FontSize',12);
legend('实际测试集分类','预测测试集分类');
title('测试集的实际分类和预测分类图','FontSize',12);
grid on;
snapnow;

%% 子函数 gaSVMcgForClass.m
function [BestCVaccuracy,Bestc,Bestg,ga_option] = gaSVMcgForClass(train_label,train_data,ga_option)
% gaSVMcgForClass

%
% by faruto
%Email:patrick.lee@foxmail.com QQ:516667408 http://blog.sina.com.cn/faruto BNU
%last modified 2010.01.17
%Super Moderator @ www.ilovematlab.cn

% 若转载请注明：
% faruto and liyang , LIBSVM-farutoUltimateVersion 
% a toolbox with implements for support vector machines based on libsvm, 2009. 
% Software available at http://www.ilovematlab.cn
% 
% Chih-Chung Chang and Chih-Jen Lin, LIBSVM : a library for
% support vector machines, 2001. Software available at
% http://www.csie.ntu.edu.tw/~cjlin/libsvm

% 参数初始化
if nargin == 2
    ga_option = struct('maxgen',200,'sizepop',20,'ggap',0.9,...
        'cbound',[0,100],'gbound',[0,1000],'v',5);
end
% maxgen:最大的进化代数,默认为200,一般取值范围为[100,500]
% sizepop:种群最大数量,默认为20,一般取值范围为[20,100]
% cbound = [cmin,cmax],参数c的变化范围,默认为(0,100]
% gbound = [gmin,gmax],参数g的变化范围,默认为[0,1000]
% v:SVM Cross Validation参数,默认为5

%
MAXGEN = ga_option.maxgen;
NIND = ga_option.sizepop;
NVAR = 2;
PRECI = 20;
GGAP = ga_option.ggap;
trace = zeros(MAXGEN,2);

FieldID = ...
[rep([PRECI],[1,NVAR]);[ga_option.cbound(1),ga_option.gbound(1);ga_option.cbound(2),ga_option.gbound(2)]; ...
 [1,1;0,0;0,1;1,1]];

Chrom = crtbp(NIND,NVAR*PRECI);

gen = 1;
v = ga_option.v;
BestCVaccuracy = 0;
Bestc = 0;
Bestg = 0;
%
cg = bs2rv(Chrom,FieldID);

for nind = 1:NIND
    cmd = ['-v ',num2str(v),' -c ',num2str(cg(nind,1)),' -g ',num2str(cg(nind,2))];
    ObjV(nind,1) = svmtrain(train_label,train_data,cmd);
end
[BestCVaccuracy,I] = max(ObjV);
Bestc = cg(I,1);
Bestg = cg(I,2);

for gen = 1:MAXGEN
    FitnV = ranking(-ObjV);
    
    SelCh = select('sus',Chrom,FitnV,GGAP);
    SelCh = recombin('xovsp',SelCh,0.7);
    SelCh = mut(SelCh);
    
    cg = bs2rv(SelCh,FieldID);
    for nind = 1:size(SelCh,1)
        cmd = ['-v ',num2str(v),' -c ',num2str(cg(nind,1)),' -g ',num2str(cg(nind,2))];
        ObjVSel(nind,1) = svmtrain(train_label,train_data,cmd);
    end
    
    [Chrom,ObjV] = reins(Chrom,SelCh,1,1,ObjV,ObjVSel);
    
    if max(ObjV) <= 50
        continue;
    end
    
    [NewBestCVaccuracy,I] = max(ObjV);
    cg_temp = bs2rv(Chrom,FieldID);
    temp_NewBestCVaccuracy = NewBestCVaccuracy;
    
    if NewBestCVaccuracy > BestCVaccuracy
       BestCVaccuracy = NewBestCVaccuracy;
       Bestc = cg_temp(I,1);
       Bestg = cg_temp(I,2);
    end
    
    if abs( NewBestCVaccuracy-BestCVaccuracy ) <= 10^(-2) && ...
        cg_temp(I,1) < Bestc
       BestCVaccuracy = NewBestCVaccuracy;
       Bestc = cg_temp(I,1);
       Bestg = cg_temp(I,2);
    end    
    
    trace(gen,1) = max(ObjV);
    trace(gen,2) = sum(ObjV)/length(ObjV);
  
end
%
figure;
hold on;
trace = round(trace*10000)/10000;
plot(trace(1:gen,1),'r*-','LineWidth',1.5);
plot(trace(1:gen,2),'o-','LineWidth',1.5);
legend('最佳适应度','平均适应度',3);
xlabel('进化代数','FontSize',12);
ylabel('适应度','FontSize',12);
axis([0 gen 0 100]);
grid on;
axis auto;

line1 = '适应度曲线Accuracy[GAmethod]';
line2 = ['(终止代数=', ...
    num2str(gen),',种群数量pop=', ...
    num2str(NIND),')'];
line3 = ['Best c=',num2str(Bestc),' g=',num2str(Bestg), ...
    ' CVAccuracy=',num2str(BestCVaccuracy),'%'];
title({
    
    line1;line2;line3},'FontSize',12);
toc

添加完毕，点击“运行”，开始仿真，输出仿真结果如下：

时间已过 15.950686 秒。
打印选择结果
Best Cross Validation Accuracy = 98.8764% Best c = 3.3514 Best g = 3.46089
Accuracy = 97.7528% (87/89) (classification)
打印测试集分类准确率
Accuracy = 97.7528% (87/89)

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3. MATLAB 仿真示例二

在当前文件夹视图中选中chapter_GridSearch.m，双击打开chapter_GridSearch.m源码如下：

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%功能：SVM的参数优化——如何更好的提升分类器的性能二
%环境：Win7，Matlab2015b
%Modi: C.S
%时间：2022-06-14
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Matlab神经网络43个案例分析

% SVM的参数优化——如何更好的提升分类器的性能
% by 李洋(faruto)
% http://www.matlabsky.com
% Email:faruto@163.com
% http://weibo.com/faruto 
% http://blog.sina.com.cn/faruto
% 2013.01.01
%% 清空环境变量
function chapter_GridSearch
close all;
clear;
clc;
format compact;
%% 数据提取
tic
% 载入测试数据wine,其中包含的数据为classnumber = 3,wine:178*13的矩阵,wine_labes:178*1的列向量
load wine.mat;

% 画出测试数据的box可视化图
figure;
boxplot(wine,'orientation','horizontal','labels',categories);
title('wine数据的box可视化图','FontSize',12);
xlabel('属性值','FontSize',12);
grid on;

% 画出测试数据的分维可视化图
figure
subplot(3,5,1);
hold on
for run = 1:178
    plot(run,wine_labels(run),'*');
end
xlabel('样本','FontSize',10);
ylabel('类别标签','FontSize',10);
title('class','FontSize',10);
for run = 2:14
    subplot(3,5,run);
    hold on;
    str = ['attrib ',num2str(run-1)];
    for i = 1:178
        plot(i,wine(i,run-1),'*');
    end
    xlabel('样本','FontSize',10);
    ylabel('属性值','FontSize',10);
    title(str,'FontSize',10);
end

% 选定训练集和测试集

% 将第一类的1-30,第二类的60-95,第三类的131-153做为训练集
train_wine = [wine(1:30,:);wine(60:95,:);wine(131:153,:)];
% 相应的训练集的标签也要分离出来
train_wine_labels = [wine_labels(1:30);wine_labels(60:95);wine_labels(131:153)];
% 将第一类的31-59,第二类的96-130,第三类的154-178做为测试集
test_wine = [wine(31:59,:);wine(96:130,:);wine(154:178,:)];
% 相应的测试集的标签也要分离出来
test_wine_labels = [wine_labels(31:59);wine_labels(96:130);wine_labels(154:178)];

%% 数据预处理
% 数据预处理,将训练集和测试集归一化到[0,1]区间

[mtrain,ntrain] = size(train_wine);
[mtest,ntest] = size(test_wine);

dataset = [train_wine;test_wine];
% mapminmax为MATLAB自带的归一化函数
[dataset_scale,ps] = mapminmax(dataset',0,1);
dataset_scale = dataset_scale';

train_wine = dataset_scale(1:mtrain,:);
test_wine = dataset_scale( (mtrain+1):(mtrain+mtest),: );
%% 选择最佳的SVM参数c&g

% 首先进行粗略选择: c&g 的变化范围是 2^(-10),2^(-9),...,2^(10)
[bestacc,bestc,bestg] = SVMcgForClass(train_wine_labels,train_wine,-10,10,-10,10);

% 打印粗略选择结果
disp('打印粗略选择结果');
str = sprintf( 'Best Cross Validation Accuracy = %g%% Best c = %g Best g = %g',bestacc,bestc,bestg);
disp(str);

% 根据粗略选择的结果图再进行精细选择: c 的变化范围是 2^(-2),2^(-1.5),...,2^(4), g 的变化范围是 2^(-4),2^(-3.5),...,2^(4),
[bestacc,bestc,bestg] = SVMcgForClass(train_wine_labels,train_wine,-2,4,-4,4,3,0.5,0.5,0.9);
% 打印精细选择结果
disp('打印精细选择结果');
str = sprintf( 'Best Cross Validation Accuracy = %g%% Best c = %g Best g = %g',bestacc,bestc,bestg);
disp(str);

%% 利用最佳的参数进行SVM网络训练
cmd = ['-c ',num2str(bestc),' -g ',num2str(bestg)];
model = svmtrain(train_wine_labels,train_wine,cmd);

%% SVM网络预测
[predict_label,accuracy] = svmpredict(test_wine_labels,test_wine,model);

% 打印测试集分类准确率
total = length(test_wine_labels);
right = sum(predict_label == test_wine_labels);
disp('打印测试集分类准确率');
str = sprintf( 'Accuracy = %g%% (%d/%d)',accuracy(1),right,total);
disp(str);

%% 结果分析

% 测试集的实际分类和预测分类图
% 通过图可以看出只有三个测试样本是被错分的
figure;
hold on;
plot(test_wine_labels,'o');
plot(predict_label,'r*');
xlabel('测试集样本','FontSize',12);
ylabel('类别标签','FontSize',12);
legend('实际测试集分类','预测测试集分类');
title('测试集的实际分类和预测分类图','FontSize',12);
grid on;
snapnow;

%% 子函数 SVMcgForClass.m
function [bestacc,bestc,bestg] = SVMcgForClass(train_label,train,cmin,cmax,gmin,gmax,v,cstep,gstep,accstep)
%SVMcg cross validation by faruto

%
% by faruto
%Email:patrick.lee@foxmail.com QQ:516667408 http://blog.sina.com.cn/faruto BNU
%last modified 2010.01.17
%Super Moderator @ www.ilovematlab.cn

% 若转载请注明：
% faruto and liyang , LIBSVM-farutoUltimateVersion 
% a toolbox with implements for support vector machines based on libsvm, 2009. 
% Software available at http://www.ilovematlab.cn
% 
% Chih-Chung Chang and Chih-Jen Lin, LIBSVM : a library for
% support vector machines, 2001. Software available at
% http://www.csie.ntu.edu.tw/~cjlin/libsvm

% about the parameters of SVMcg 
if nargin < 10
    accstep = 4.5;
end
if nargin < 8
    cstep = 0.8;
    gstep = 0.8;
end
if nargin < 7
    v = 5;
end
if nargin < 5
    gmax = 8;
    gmin = -8;
end
if nargin < 3
    cmax = 8;
    cmin = -8;
end
% X:c Y:g cg:CVaccuracy
[X,Y] = meshgrid(cmin:cstep:cmax,gmin:gstep:gmax);
[m,n] = size(X);
cg = zeros(m,n);

eps = 10^(-4);

% record acc with different c & g,and find the bestacc with the smallest c
bestc = 1;
bestg = 0.1;
bestacc = 0;
basenum = 2;
for i = 1:m
    for j = 1:n
        cmd = ['-v ',num2str(v),' -c ',num2str( basenum^X(i,j) ),' -g ',num2str( basenum^Y(i,j) )];
        cg(i,j) = svmtrain(train_label, train, cmd);
        
        if cg(i,j) <= 55
            continue;
        end
        
        if cg(i,j) > bestacc
            bestacc = cg(i,j);
            bestc = basenum^X(i,j);
            bestg = basenum^Y(i,j);
        end        
        
        if abs( cg(i,j)-bestacc )<=eps && bestc > basenum^X(i,j) 
            bestacc = cg(i,j);
            bestc = basenum^X(i,j);
            bestg = basenum^Y(i,j);
        end        
        
    end
end
% to draw the acc with different c & g
figure;
[C,h] = contour(X,Y,cg,70:accstep:100);
clabel(C,h,'Color','r');
xlabel('log2c','FontSize',12);
ylabel('log2g','FontSize',12);
firstline = 'SVC参数选择结果图(等高线图)[GridSearchMethod]'; 
secondline = ['Best c=',num2str(bestc),' g=',num2str(bestg), ...
    ' CVAccuracy=',num2str(bestacc),'%'];
title({
    
    firstline;secondline},'Fontsize',12);
grid on; 

figure;
meshc(X,Y,cg);
% mesh(X,Y,cg);
% surf(X,Y,cg);
axis([cmin,cmax,gmin,gmax,30,100]);
xlabel('log2c','FontSize',12);
ylabel('log2g','FontSize',12);
zlabel('Accuracy(%)','FontSize',12);
firstline = 'SVC参数选择结果图(3D视图)[GridSearchMethod]'; 
secondline = ['Best c=',num2str(bestc),' g=',num2str(bestg), ...
    ' CVAccuracy=',num2str(bestacc),'%'];
title({
    
    firstline;secondline},'Fontsize',12);
toc

点击“运行”，开始仿真，输出仿真结果如下：

时间已过 6.247385 秒。
打印粗略选择结果
Best Cross Validation Accuracy = 98.8764% Best c = 2.2974 Best g = 4
时间已过 6.746255 秒。
打印精细选择结果
Best Cross Validation Accuracy = 98.8764% Best c = 1.41421 Best g = 1
Accuracy = 98.8764% (88/89) (classification)
打印测试集分类准确率
Accuracy = 98.8764% (88/89)

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4. MATLAB 仿真示例三

在当前文件夹视图中选中chapter_PSO.m，双击打开chapter_PSO.m源码如下：

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%功能：SVM的参数优化——如何更好的提升分类器的性能三
%环境：Win7，Matlab2015b
%Modi: C.S
%时间：2022-06-14
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% Matlab神经网络43个案例分析

% SVM的参数优化——如何更好的提升分类器的性能
% by 李洋(faruto)
% http://www.matlabsky.com
% Email:faruto@163.com
% http://weibo.com/faruto 
% http://blog.sina.com.cn/faruto
% 2013.01.01
%% 清空环境变量
function chapter_PSO
close all;
clear;
clc;
format compact;
%% 数据提取
tic
% 载入测试数据wine,其中包含的数据为classnumber = 3,wine:178*13的矩阵,wine_labes:178*1的列向量
load wine.mat;

% 画出测试数据的box可视化图
figure;
boxplot(wine,'orientation','horizontal','labels',categories);
title('wine数据的box可视化图','FontSize',12);
xlabel('属性值','FontSize',12);
grid on;

% 画出测试数据的分维可视化图
figure
subplot(3,5,1);
hold on
for run = 1:178
    plot(run,wine_labels(run),'*');
end
xlabel('样本','FontSize',10);
ylabel('类别标签','FontSize',10);
title('class','FontSize',10);
for run = 2:14
    subplot(3,5,run);
    hold on;
    str = ['attrib ',num2str(run-1)];
    for i = 1:178
        plot(i,wine(i,run-1),'*');
    end
    xlabel('样本','FontSize',10);
    ylabel('属性值','FontSize',10);
    title(str,'FontSize',10);
end

% 选定训练集和测试集

% 将第一类的1-30,第二类的60-95,第三类的131-153做为训练集
train_wine = [wine(1:30,:);wine(60:95,:);wine(131:153,:)];
% 相应的训练集的标签也要分离出来
train_wine_labels = [wine_labels(1:30);wine_labels(60:95);wine_labels(131:153)];
% 将第一类的31-59,第二类的96-130,第三类的154-178做为测试集
test_wine = [wine(31:59,:);wine(96:130,:);wine(154:178,:)];
% 相应的测试集的标签也要分离出来
test_wine_labels = [wine_labels(31:59);wine_labels(96:130);wine_labels(154:178)];

%% 数据预处理
% 数据预处理,将训练集和测试集归一化到[0,1]区间

[mtrain,ntrain] = size(train_wine);
[mtest,ntest] = size(test_wine);

dataset = [train_wine;test_wine];
% mapminmax为MATLAB自带的归一化函数
[dataset_scale,ps] = mapminmax(dataset',0,1);
dataset_scale = dataset_scale';

train_wine = dataset_scale(1:mtrain,:);
test_wine = dataset_scale( (mtrain+1):(mtrain+mtest),: );
%% 选择最佳的SVM参数c&g

[bestacc,bestc,bestg] = psoSVMcgForClass(train_wine_labels,train_wine);

% 打印选择结果
disp('打印选择结果');
str = sprintf( 'Best Cross Validation Accuracy = %g%% Best c = %g Best g = %g',bestacc,bestc,bestg);
disp(str);

%% 利用最佳的参数进行SVM网络训练
cmd = ['-c ',num2str(bestc),' -g ',num2str(bestg)];
model = svmtrain(train_wine_labels,train_wine,cmd);

%% SVM网络预测
[predict_label,accuracy] = svmpredict(test_wine_labels,test_wine,model);

% 打印测试集分类准确率
total = length(test_wine_labels);
right = sum(predict_label == test_wine_labels);
disp('打印测试集分类准确率');
str = sprintf( 'Accuracy = %g%% (%d/%d)',accuracy(1),right,total);
disp(str);

%% 结果分析

% 测试集的实际分类和预测分类图
% 通过图可以看出只有三个测试样本是被错分的
figure;
hold on;
plot(test_wine_labels,'o');
plot(predict_label,'r*');
xlabel('测试集样本','FontSize',12);
ylabel('类别标签','FontSize',12);
legend('实际测试集分类','预测测试集分类');
title('测试集的实际分类和预测分类图','FontSize',12);
grid on;
snapnow;

%% 子函数 psoSVMcgForClass.m
function [bestCVaccuarcy,bestc,bestg,pso_option] = psoSVMcgForClass(train_label,train,pso_option)
% psoSVMcgForClass

%
% by faruto
%Email:patrick.lee@foxmail.com QQ:516667408 http://blog.sina.com.cn/faruto BNU
%last modified 2010.01.17
%Super Moderator @ www.ilovematlab.cn

% 若转载请注明：
% faruto and liyang , LIBSVM-farutoUltimateVersion 
% a toolbox with implements for support vector machines based on libsvm, 2009. 
% Software available at http://www.ilovematlab.cn
% 
% Chih-Chung Chang and Chih-Jen Lin, LIBSVM : a library for
% support vector machines, 2001. Software available at
% http://www.csie.ntu.edu.tw/~cjlin/libsvm
% 参数初始化
if nargin == 2
    pso_option = struct('c1',1.5,'c2',1.7,'maxgen',200,'sizepop',20, ...
        'k',0.6,'wV',1,'wP',1,'v',5, ...
        'popcmax',10^2,'popcmin',10^(-1),'popgmax',10^3,'popgmin',10^(-2));
end
% c1:初始为1.5,pso参数局部搜索能力
% c2:初始为1.7,pso参数全局搜索能力
% maxgen:初始为200,最大进化数量
% sizepop:初始为20,种群最大数量
% k:初始为0.6(k belongs to [0.1,1.0]),速率和x的关系(V = kX)
% wV:初始为1(wV best belongs to [0.8,1.2]),速率更新公式中速度前面的弹性系数
% wP:初始为1,种群更新公式中速度前面的弹性系数
% v:初始为3,SVM Cross Validation参数
% popcmax:初始为100,SVM 参数c的变化的最大值.
% popcmin:初始为0.1,SVM 参数c的变化的最小值.
% popgmax:初始为1000,SVM 参数g的变化的最大值.
% popgmin:初始为0.01,SVM 参数c的变化的最小值.

Vcmax = pso_option.k*pso_option.popcmax;
Vcmin = -Vcmax ;
Vgmax = pso_option.k*pso_option.popgmax;
Vgmin = -Vgmax ;

eps = 10^(-3);

% 产生初始粒子和速度
for i=1:pso_option.sizepop
    
    % 随机产生种群和速度
    pop(i,1) = (pso_option.popcmax-pso_option.popcmin)*rand+pso_option.popcmin;
    pop(i,2) = (pso_option.popgmax-pso_option.popgmin)*rand+pso_option.popgmin;
    V(i,1)=Vcmax*rands(1,1);
    V(i,2)=Vgmax*rands(1,1);
    
    % 计算初始适应度
    cmd = ['-v ',num2str(pso_option.v),' -c ',num2str( pop(i,1) ),' -g ',num2str( pop(i,2) )];
    fitness(i) = svmtrain(train_label, train, cmd);
    fitness(i) = -fitness(i);
end

% 找极值和极值点
[global_fitness bestindex]=min(fitness); % 全局极值
local_fitness=fitness;   % 个体极值初始化

global_x=pop(bestindex,:);   % 全局极值点
local_x=pop;    % 个体极值点初始化

% 每一代种群的平均适应度
avgfitness_gen = zeros(1,pso_option.maxgen);

% 迭代寻优
for i=1:pso_option.maxgen
    
    for j=1:pso_option.sizepop
        
        %速度更新
        V(j,:) = pso_option.wV*V(j,:) + pso_option.c1*rand*(local_x(j,:) - pop(j,:)) + pso_option.c2*rand*(global_x - pop(j,:));
        if V(j,1) > Vcmax
            V(j,1) = Vcmax;
        end
        if V(j,1) < Vcmin
            V(j,1) = Vcmin;
        end
        if V(j,2) > Vgmax
            V(j,2) = Vgmax;
        end
        if V(j,2) < Vgmin
            V(j,2) = Vgmin;
        end
        
        %种群更新
        pop(j,:)=pop(j,:) + pso_option.wP*V(j,:);
        if pop(j,1) > pso_option.popcmax
            pop(j,1) = pso_option.popcmax;
        end
        if pop(j,1) < pso_option.popcmin
            pop(j,1) = pso_option.popcmin;
        end
        if pop(j,2) > pso_option.popgmax
            pop(j,2) = pso_option.popgmax;
        end
        if pop(j,2) < pso_option.popgmin
            pop(j,2) = pso_option.popgmin;
        end
        
        % 自适应粒子变异
        if rand>0.5
            k=ceil(2*rand);
            if k == 1
                pop(j,k) = (20-1)*rand+1;
            end
            if k == 2
                pop(j,k) = (pso_option.popgmax-pso_option.popgmin)*rand + pso_option.popgmin;
            end
        end
        
        %适应度值
        cmd = ['-v ',num2str(pso_option.v),' -c ',num2str( pop(j,1) ),' -g ',num2str( pop(j,2) )];
        fitness(j) = svmtrain(train_label, train, cmd);
        fitness(j) = -fitness(j);
        
        cmd_temp = ['-c ',num2str( pop(j,1) ),' -g ',num2str( pop(j,2) )];
        model = svmtrain(train_label, train, cmd_temp);
        
        if fitness(j) >= -65
            continue;
        end
        
        %个体最优更新
        if fitness(j) < local_fitness(j)
            local_x(j,:) = pop(j,:);
            local_fitness(j) = fitness(j);
        end
        
        if abs( fitness(j)-local_fitness(j) )<=eps && pop(j,1) < local_x(j,1)
            local_x(j,:) = pop(j,:);
            local_fitness(j) = fitness(j);
        end
        
        %群体最优更新
        if fitness(j) < global_fitness
            global_x = pop(j,:);
            global_fitness = fitness(j);
        end
        
        if abs( fitness(j)-global_fitness )<=eps && pop(j,1) < global_x(1)
            global_x = pop(j,:);
            global_fitness = fitness(j);
        end
        
    end
    
    fit_gen(i) = global_fitness;
    avgfitness_gen(i) = sum(fitness)/pso_option.sizepop;
end

% 结果分析
figure;
hold on;
plot(-fit_gen,'r*-','LineWidth',1.5);
plot(-avgfitness_gen,'o-','LineWidth',1.5);
legend('最佳适应度','平均适应度',3);
xlabel('进化代数','FontSize',12);
ylabel('适应度','FontSize',12);
grid on;

bestc = global_x(1);
bestg = global_x(2);
bestCVaccuarcy = -fit_gen(pso_option.maxgen);

line1 = '适应度曲线Accuracy[PSOmethod]';
line2 = ['(参数c1=',num2str(pso_option.c1), ...
    ',c2=',num2str(pso_option.c2),',终止代数=', ...
    num2str(pso_option.maxgen),',种群数量pop=', ...
    num2str(pso_option.sizepop),')'];
line3 = ['Best c=',num2str(bestc),' g=',num2str(bestg), ...
    ' CVAccuracy=',num2str(bestCVaccuarcy),'%'];
title({
    
    line1;line2;line3},'FontSize',12);
toc

点击“运行”，开始仿真，输出仿真结果如下：

时间已过 27.758234 秒。
打印选择结果
Best Cross Validation Accuracy = 98.8764% Best c = 78.4233 Best g = 2.94625
Accuracy = 98.8764% (88/89) (classification)
打印测试集分类准确率
Accuracy = 98.8764% (88/89)

在这里插入图片描述
在这里插入图片描述
在这里插入图片描述
在这里插入图片描述

5. 小结

本文介绍通过常见的优化算法（遗传算法、蚁群算法等）对SVM的参数进行优化，再进行分类测试的示例，可以看到经过参数优化后的分类效果，记得此前自己进行分类器的参数选择时，一般都是通过不断遍历进行实验，最终找到性能最佳的参数作为最佳参数，其实效率实在有待提升，这里看到通过优化算法进行参数调优，确实眼前一亮。对本章内容感兴趣或者想充分学习了解的，建议去研习书中第十五章节的内容。后期会对其中一些知识点在自己理解的基础上进行补充，欢迎大家一起学习交流。

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