SVM实现一个三类分类问题

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#此前在首页部分显示#

——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;