1.软件版本

MATLAB2013b
2.本算法理论知识

[1] Lee Y , Lin Y , Wahba G . Multicategory support vector machines. 2001.A05-15
3.部分源码

clc;
clear;
close all;
warning off;
pack;
addpath 'func\'
RandStream.setDefaultStream(RandStream('mt19937ar','seed',8));

%产生测试数据源
%产生测试数据源
Class_Num = 5;  %原始数据类别数,>=2 , <= 10
Num       = 20; %数据个数
Xt        = [];
Yt        = [];
Lt        = [];
colors{1} = 'bo';
colors{2} = 'r*';
colors{3} = 'gx';
colors{4} = 'k+';
colors{5} = 'ms';
colors{6} = 'c^';
colors{7} = 'y>';
colors{8} = 'b*';
colors{9} = 'rx';
colors{10}= 'ms';

figure;
subplot(131);
for i = 1:Class_Num
    %测试数据设置为1维，2维，或者3维，多维测试数据不方便观察
    Nums= 10+round(Num*rand(1))+1;
    Xo  = 3*floor((i+1)/2) + randn(1,Nums);
    Yo  = 3*mod(i,2)       + randn(1,Nums);
    Lo  = i*ones(1,Nums);
    Xt  = [Xt,Xo];
    Yt  = [Yt,Yo];  
    Lt  = [Lt,Lo];
    plot(Xo,Yo,colors{1});
    hold on;
end
title('原始数据');  
Test_Dat = [Xt;Yt]; 
Category = Lt;
axis square;
Len_xy   = axis;
axis([Len_xy(1),Len_xy(2),Len_xy(3),Len_xy(4)]);

subplot(132);
func_MSVM_old(Test_Dat,Category,Class_Num,colors,Len_xy);


 
%%newmsvm
%%newmsvm
%%newmsvm
%根据MSVM论文的算法进行多分类SVM仿真
%进行训练
Parameter.solver ='Operation';
Parameter.ker    ='linear';
Parameter.arg    = 1;
Parameter.C      = 1;
[dim,num_data]   = size(Test_Dat);
CNT              = 0;
Category_Index   = [];
Classes          = zeros(2,(Class_Num-1)*Class_Num/2);
Alpha            = zeros(num_data,(Class_Num-1)*Class_Num/2);
b                = zeros((Class_Num-1)*Class_Num/2,1);
K                = 0;

Test_Dat1        = Test_Dat;
Test_Dat2        = Test_Dat.^2;
Test_Dat3        = [Test_Dat(1,:).*Test_Dat(2,:);Test_Dat(1,:).*Test_Dat(2,:)];
bin_model        = [];
Alpha1           = zeros(num_data,(Class_Num-1)*Class_Num/2);
b1               = zeros((Class_Num-1)*Class_Num/2,1);
K1               = 0;
for j1 = 1:Class_Num-1
    for j2 = j1+1:Class_Num
        CNT = CNT + 1
        %dual form
        Classes(1,CNT) = j1;
        Classes(2,CNT) = j2;
        Category_Index1= find(Category==j1);
        Category_Index2= find(Category==j2);
        Category_Index = unique([Category_Index1,Category_Index2]);
        bin_data.X     = Test_Dat1(:,Category_Index);
        bin_data.y     = Category(:,Category_Index);
        bin_data.y(find(bin_data.y == j1)) = 1;
        bin_data.y(find(bin_data.y == j2)) = 2;
        bin_model      = feval('Operation',bin_data,Parameter);
        %计算alpha
        Alpha1(Category_Index(bin_model.POS.inx),CNT) = bin_model.Alpha(:);
        %计算b
        b1(CNT) = bin_model.b;
        %计算K
        K1      = K1 + bin_model.K;
    end
end
bin_model        = [];
CNT              = 0;
Category_Index   = [];
Alpha2           = zeros(num_data,(Class_Num-1)*Class_Num/2);
b2               = zeros((Class_Num-1)*Class_Num/2,1);
K2               = 0;
for j1 = 1:Class_Num-1
    for j2 = j1+1:Class_Num
        CNT = CNT + 1
        %dual form
        Classes(1,CNT) = j1;
        Classes(2,CNT) = j2;
        Category_Index1= find(Category==j1);
        Category_Index2= find(Category==j2);
        Category_Index = unique([Category_Index1,Category_Index2]);
        bin_data.X     = Test_Dat2(:,Category_Index);
        bin_data.y     = Category(:,Category_Index);
        bin_data.y(find(bin_data.y == j1)) = 1;
        bin_data.y(find(bin_data.y == j2)) = 2;
        bin_model      = feval('Operation',bin_data,Parameter);
        %计算alpha
        Alpha2(Category_Index(bin_model.POS.inx),CNT) = bin_model.Alpha(:);
        %计算b
        b2(CNT) = bin_model.b;
        %计算K
        K2     = K2 + bin_model.K;
    end
end
bin_model        = [];
CNT              = 0;
Category_Index   = [];
Alpha3           = zeros(num_data,(Class_Num-1)*Class_Num/2);
b3               = zeros((Class_Num-1)*Class_Num/2,1);
K3               = 0;
for j1 = 1:Class_Num-1
    for j2 = j1+1:Class_Num
        CNT = CNT + 1
        %dual form
        Classes(1,CNT) = j1;
        Classes(2,CNT) = j2;
        Category_Index1= find(Category==j1);
        Category_Index2= find(Category==j2);
        Category_Index = unique([Category_Index1,Category_Index2]);
        bin_data.X     = Test_Dat3(:,Category_Index);
        bin_data.y     = Category(:,Category_Index);
        bin_data.y(find(bin_data.y == j1)) = 1;
        bin_data.y(find(bin_data.y == j2)) = 2;
        bin_model      = feval('Operation',bin_data,Parameter);
        %计算alpha
        Alpha3(Category_Index(bin_model.POS.inx),CNT) = bin_model.Alpha(:);
        %计算b
        b3(CNT) = bin_model.b;
        %计算K
        K3      = K3 + bin_model.K;
    end
end

Alphao{1} = Alpha1;
Alphao{2} = Alpha2;
Alphao{3} = Alpha3;
bo{1}     = b1;
bo{2}     = b2;
bo{3}     = b3;
Ko{1}     = K1;
Ko{2}     = K2;
Ko{3}     = K3;

[V,I] = min([K1(1),K2(1),K3(1)]);
K     = Ko{I};

Alpha = Alphao{I};
b     = bo{I};



index0             = find(sum(abs(Alpha),2)~= 0);
MSVM_Net.Alpha     = Alpha(index0,:);
MSVM_Net.b         = b;
MSVM_Net.Classes   = Classes;
MSVM_Net.Pos.X     = Test_Dat(:,index0);
MSVM_Net.Pos.y     = Category(index0);
MSVM_Net.K         = K;
MSVM_Net.Parameter = Parameter;
 
subplot(133);
DIM = size(Test_Dat,1);
for Class_Ind = 1:Class_Num
    Index = find(Category == Class_Ind);
    if isempty(Index)==0
       if DIM == 1
          h = plot(Test_Dat(1,Index),zeros(1,length(Index)),colors{Class_Ind});
       end
       if DIM == 2
          h = plot(Test_Dat(1,Index),Test_Dat(2,Index),colors{Class_Ind});
       end
       if DIM >= 3
          h = plot3(Test_Dat(1,Index),Test_Dat(2,Index),Test_Dat(3,Index),colors{Class_Ind});
       end
    end
    hold on;
end

dx        = 0.1;
dy        = 0.1;
Xgrid     = Len_xy(1):dx:Len_xy(2);
Ygrid     = Len_xy(3):dy:Len_xy(4);
[X,Y]     = meshgrid(Xgrid,Ygrid);

Xmulti    = 1;
Ymulti    = 1;
for j = 1:DIM
    Xmulti = Xmulti*size(X,j);
    Ymulti = Ymulti*size(Y,j);
end         
View_data = [reshape(X',1,Xmulti);
             reshape(Y',1,Ymulti)];     
         
MSVM_     = feval('msvmclassify',View_data,MSVM_Net);

%计算分类错误概率
Ini_Class = Category;
Label_test= msvmclassify(Test_Dat,MSVM_Net);
Label_init= Ini_Class;
Error     = length(find((Label_test-Label_init)~=0))/length(Label_test);
Dats      = num2str(100*Error);

func_get_boudary(MSVM_,Class_Num,Xgrid,Ygrid);
title(['错误比例:',Dats,'%']);  
axis square;
axis([Len_xy(1),Len_xy(2),Len_xy(3),Len_xy(4)]);

clc;
clear;