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
            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
            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
            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
            end         
            
            for i=1:length(f)
                if(testgroup(i)~=f(i))
                    ErrorNum = ErrorNum + 1;
                end
            end          
        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
        
    end
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
        r
        c
        correct5
        if(fcorrect<correct5)
            fcorrect=correct5
            fr=r
            fc=c
        end
        correct5=0;
    end
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