function svm = svmTrain(svmType,X,Y,ker,p1,p2)
% SVM Classification:
% svm = svmTrain('svc_c',x,y,ker,C);
% svm = svmTrain('svc_nu',x,y,ker,nu);
%
% One-Class SVM:
% svm = svmTrain('svm_one_class',x,[],ker,nu);
%
% SVM Regression:
% svm = svmTrain('svr_epsilon',x,y,ker,C,e);
% svm = svmTrain('svr_nu',x,y,ker,C,nu);
% 输入参数:
% X 训练样本,d×n的矩阵,n为样本个数,d为样本维数
% Y 训练目标,1×n的矩阵,n为样本个数,值为+1或-1
% ker 核参数(结构体变量)
% the following fields:
% type - linear : k(x,y) = x'*y
% poly : k(x,y) = (x'*y+c)^d
% gauss : k(x,y) = exp(-0.5*(norm(x-y)/s)^2)
% tanh : k(x,y) = tanh(g*x'*y+c)
% degree - Degree d of polynomial kernel (positive scalar).
% offset - Offset c of polynomial and tanh kernel (scalar, negative for tanh).
% width - Width s of Gauss kernel (positive scalar).
% gamma - Slope g of the tanh kernel (positive scalar).
% 输出参数:
% svm 支持向量机(结构体变量)
% the following fields:
% type - 支持向量机类型 {
'svc_c','svc_nu','svm_one_class','svr_epsilon','svr_nu'
}
% ker - 核参数
% x - 训练样本,d×n的矩阵,n为样本个数,d为样本维数
% y - 训练目标,1×n的矩阵,n为样本个数,值为+1或-1
% a - 拉格朗日乘子,1×n的矩阵
% ------------------------------------------------------------%
options = optimset;
options.LargeScale = 'off';
options.Display = 'off';
switch svmType
case 'svc_c',
C = p1;
n = length(Y);
H = (Y'*Y).*kernel(ker,X,X);
f = -ones(n,1);
A = [];
b = [];
Aeq = Y;
beq = 0;
lb = zeros(n,1);
ub = C*ones(n,1);
a0 = zeros(n,1);
[a,fval,eXitflag,output,lambda] = quadprog(H,f,A,b,Aeq,beq,lb,ub,a0,options);
case 'svc_nu',
nu = p1;
n = length(Y);
H = (Y'*Y).*kernel(ker,X,X);
f = zeros(n,1);
A = -ones(1,n);
b = -nu;
Aeq = Y;
beq = 0;
lb = zeros(n,1);
ub = ones(n,1)/n;
a0 = zeros(n,1);
[a,fval,eXitflag,output,lambda] = quadprog(H,f,A,b,Aeq,beq,lb,ub,a0,options);
case 'svm_one_class',
nu = p1;
n = size(X,2);
H = kernel(ker,X,X);
f = zeros(n,1);
for i = 1:n
f(i,:) = -kernel(ker,X(:,i),X(:,i));
end
A = [];
b = [];
Aeq = ones(1,n);
beq = 1;
lb = zeros(n,1);
ub = ones(n,1)/(nu*n);
a0 = zeros(n,1);
[a,fval,eXitflag,output,lambda] = quadprog(H,f,A,b,Aeq,beq,lb,ub,a0,options);
case 'svr_epsilon',
C = p1;
e = p2;
n = length(Y);
Q = kernel(ker,X,X);
H = [Q,-Q;-Q,Q];
f = [e*ones(n,1)-Y';e*ones(n,1)+Y']; % 符号不一样,决策函数就不一样,实际上是一回事!
%f = [e*ones(n,1)+Y';e*ones(n,1)-Y'];
A = [];
b = [];
Aeq = [ones(1,n),-ones(1,n)];
beq = 0;
lb = zeros(2*n,1);
ub = C*ones(2*n,1);
a0 = zeros(2*n,1);
[a,fval,eXitflag,output,lambda] = quadprog(H,f,A,b,Aeq,beq,lb,ub,a0,options);
a = a(1:n)-a(n+1:end);
case 'svr_nu',
C = p1;
nu = p2;
n = length(Y);
Q = kernel(ker,X,X);
H = [Q,-Q;-Q,Q];
f = [-Y';+Y']; % 符号不一样,决策函数就不一样,实际上是一回事!
%f = [+Y';-Y'];
A = [];
b = [];
Aeq = [ones(1,n),-ones(1,n);ones(1,2*n)];
beq = [0;C*n*nu];
lb = zeros(2*n,1);
ub = C*ones(2*n,1);
a0 = zeros(2*n,1);
[a,fval,eXitflag,output,lambda] = quadprog(H,f,A,b,Aeq,beq,lb,ub,a0,options);
a = a(1:n)-a(n+1:end);
otherwise,
end
eXitflag
% ------------------------------------------------------------%
% 输出 svm
svm.type = svmType;
svm.ker = ker;
svm.x = X;
svm.y = Y;
svm.a = a';
