利用SVM实现一个三类分类问题

一．任务要求

用SVM求解一个三类分类问题，实验数据为“鸢尾属植物数据集”，核函数为径向基核函数（RBF），误差评测标准为K折交叉确认误差。

二．实验方案

1．用quadprog函数实现C-SVC来进行分类

——quadprog是matlab中一个求解二次规划的函数，通过适当的参数设置，可以利用quadprog函数实现C-SVC

2．用matlab自带的SVM工具包来实现分类

——matlab2006版本中集成了SVM工具包，可以通过调用工具包中的svmtrain和svmclassify函数来进行训练和分类

3．三类问题的分类方法

——将三类问题转化为三个两类问题，分别求出相应的决策函数即可（优点：方法简单易行；缺点：容易形成死区）

三．实验程序

1．用Quadprog实现

clear all

% Load the data and select features for classification

load fisheriris;

data = meas;

% Get the size of the data

N = size(data, 1 );

% Extract the Setosa class

groups_temp = ismember(species, ' versicolor ' ); % versicolor,virginica,setosa

% convert the group to 1 & - 1

groups = 2 * groups_temp - ones(N, 1 );

indices = crossvalind( ' Kfold ' , groups);

ErrorMin = 1 ;

for r = 1 : 1 : 5

for C = 1 : 1 : 5

ErrorNum = 0 ;

for i = 1 : 5

% Use K - fold to get train data and test data

test = (indices == i); train = ~ test;

traindata = data(train,:);

traingroup = groups(train,:);

trainlength = length(traingroup);

testdata = data(test,:);

testgroup = groups(test,:);

testlength = length(testgroup);

% Get matrix H of the problem

kfun = [];

for i = 1 : 1 :trainlength

for j = 1 : 1 :trainlength

% rbf kernel

kfun(i,j) = exp( - 1 / (r ^ 2 ) * (traindata(i,:) - traindata(j,:)) * (traindata(i,:) - traindata(j,:)) ' );

end

% count parameters of quadprog function

H = (traingroup * traingroup ' ).*kfun;

xstart = zeros(trainlength, 1 );

f = - ones(trainlength, 1 );

Aeq = traingroup ' ;

beq = 0 ;

lb = zeros(trainlength, 1 );

ub = C * ones(trainlength, 1 );

[alpha,fval] = quadprog(H,f,[],[],Aeq,beq,lb,ub,xstart);

% Get one of the non - zero part of vector alpha to count b

j = 1 ;

for i = 1 :size(alpha)

if (alpha(i) > (1e - 5 ))

SvmClass_temper(j,:) = traingroup(i);

SvmAlpha_temper(j,:) = alpha(i);

SvmVector_temper(j,:) = traindata(i,:);

j = j + 1 ;

tag = i;

end

b = traingroup(tag) - (alpha. * traingroup) ' *kfun(:,tag);

% Use the function to test the test data

kk = [];

for i = 1 :testlength

for j = 1 :trainlength

kk(i,j) = exp( - 1 / (r ^ 2 ) * (testdata(i,:) - traindata(j,:)) * (testdata(i,:) - traindata(j,:)) ' );

end

% then count the function

f = (alpha. * traingroup) ' *kk ' + b;

for i = 1 :length(f)

if (f(i) > (1e - 5 ))

f(i) = 1 ;

else

f(i) =- 1 ;

end

for i = 1 :length(f)

if (testgroup(i) ~= f(i))

ErrorNum = ErrorNum + 1 ;

end

ErrorRate = ErrorNum / N;

if (ErrorRate < ErrorMin)

SvmClass = SvmClass_temper;

SvmAlpha = SvmAlpha_temper;

SvmVector = SvmVector_temper;

ErrorMin = ErrorRate;

CorrectRate = 1 - ErrorRate;

Coptimal = C;

Roptimal = r;

end

2．用SVM工具包实现

clear all

% Load the data and select features for classification

load fisheriris

% data = [meas(:, 3 ),meas(:, 4 )];

data = meas;

% Extract the Setosa class

groups = ismember(species, ' versicolor ' ); % versicolor,virginica,setosa

% Randomly select training and test sets

index = crossvalind( ' Kfold ' ,groups);

cp = classperf(groups);

fr = 0 ;

fc = 0 ;

fcorrect = 0 ;

correct5 = 0 ;

for r = 1 : 1 : 10

for c = 1 : 1 : 100

for i = 1 : 5

test = (index == i); train = ~ test;

% Use a RBF support vector machine classifier

% svmStruct = svmtrain(data(train,:),groups(train), ' KERNEL_FUNCTION ' , ' rbf ' , ' kfunargs ' , 5 , ' boxconstraint ' , 1000 , ' showplot ' , true );

% classes = svmclassify(svmStruct,data(test,:), ' showplot ' , true );

svmStruct = svmtrain(data(train,:),groups(train), ' KERNEL_FUNCTION ' , ' rbf ' , ' kfunargs ' , 1 / (r ^ 2 ), ' boxconstraint ' ,c);

classes = svmclassify(svmStruct,data(test,:));

% See how well the classifier performed

classperf(cp,classes,test);

% cp.CorrectRate

correct5 = correct5 + cp.CorrectRate / 5 ;

end

correct5

if (fcorrect < correct5)

fcorrect = correct5

fr = r

fc = c

end

correct5 = 0 ;

end

四．实验结果

1． Quadprog实现

(1)类别：versicolor 参数：r(1-10) C(1-100)

运行结果：

CorrectRate =0.9696 Roptimal =1 Coptimal =2

(2)类别：virginica 参数：r(1-10) C(1-100)

运行结果：

CorrectRate =0.9430 Roptimal =1 Coptimal =2

(3)类别：setosa 参数：r(1-10) C(1-100)

运行结果：

CorrectRate =1 Roptimal =1 Coptimal =1

2． SVM工具包实现

(1)类别：versicolor 参数：r(1-5) C(1-50)

运行结果：

CorrectRate =1 Roptimal =2 Coptimal =22

(2)类别：virginica 参数：r(1-5) C(1-50)

运行结果：

CorrectRate =0.9867 Roptimal =10 Coptimal =44

(3)类别：setosa 参数：r(1-10) C(1-100)

运行结果：

CorrectRate =1 Roptimal =1 Coptimal =1

原文链接：https://blog.csdn.net/Afei_ia_hw/article/details/1587356