linsvm.m

四种支持向量机用于函数拟合与模式识别的Matlab示例程序

function [alpha,theta,solution]=linsvm(X,J)
% LINSVM Support Vector Machines for the linear and separable case.
%  [alpha,theta,solution]=linsvm(X,J)
%
% LINSVM is an implementation of the Support Vector Machines 
%  method for the linear and separable case. It finds a vector 
%  alpha and a threshold which solve following task  
% 
%   1)  alpha' * x >= theta    for x=X(:,i), J(i)=1, (1st class)
%       alpha' * x < theta     for x=X(:,i), J(i)=2, (2nd class)
%
%   2) and a margin between point sets (their convex hulls) 
%      is maximal.
%
%  The algorithm transforms the problem mentioned above to the
%  equivalent problem of quadratic programing and uses Matlab
%  Optimization Toolbox for resolving.
%
%  Input:
%   X [DxM] contains M training points in the D-dimensional 
%     feature space. X=[x1,x2,..XM] where xi is i-th column vectors.
%   J [1xM] contains class labels of the points in X. A class
%     label must be 1 for the first class and 2 for the second class.
%
%  Output:
%   alpha [Dx1] normal vector of the found decision hyperplane.
%   theta [1x1] threshold of the found hyperplane.
%   solution [1x1], 1 ... solution is found,
%                   0 ... solution is not found.
%
% See also PERCEPTR, KOZINEC, EKOZINEC.
%

% Statistical Pattern Recognition Toolbox, Vojtech Franc, Vaclav Hlavac
% (c) Czech Technical University Prague, http://cmp.felk.cvut.cz
% Written Vojtech Franc (diploma thesis) 02.11.1999, 17.01.2000, 13.4.2000
% Modifications
% 24. 6.00 V. Hlavac, comments polished.
% 16-dec-2000, comments repaired

% Transform original feature space into the homogenous (theta=0)
% coordinates.
[alpha,X]=ctransf(0,0,X,J);

N=size(X,1);   % dimension
K=size(X,2);   % number of training points.

% Transform the problem to the quadratic programming problem
% min x'*H*x+f'*x   ,   A*x <= b
%  x
%-------------------------------------------

H=eye(N);
f=zeros(N,1);
b=-ones(K,1);
A=-X';

% Call quadratic programming method
%-----------------------------------------------
[alpha,lag,how]=qp(H,f,A,b,[],[],[],0,-1);

% Transform the found solution from the homogenous coordinates
% into original space.
[alpha,theta]=ictransf(alpha);

% Set solution according to the qp result
%----------------------------------------
if strcmpi(how,'ok')==1,
   solution=1;
else
   solution=0;
end