spca.m

this a SVM toolbox,it is very useful for someone who just learn SVM.In order to be undestood easily,

function [T,sumeigv,eigv] = spca(X,m,method)
% SPCA Principal Component Analysis.
%  [T,sumeigv,eigv] = spca(X,m,method)
%
% SPCA is the standard Principal Componets Analysis (PCA). 
%   The original d-dimensional feature space is reduced into 
%   new m-dimensional space (m < d) by a linear transfomation
%          y = T*x
%
%   where x is d-dimensional vector from the original space and
%   y is m-dimensional from the reduced space. The rows of the 
%   matrix T contains eigenvetors of covariance matrix of data X.
%   The eigenvectors are ordered according to their eigenvalues 
%   in descending order.
%
%   Two methods of decomposition to eigenspace are used:
%     1) method = 'default'  uses eig( cov( X' )), better for d << l
%     2) method = 'ecov'  uses ecov (see help ecov), better for d >> l
%   where l is the number of input data.
%
% Input: 
%  X [d x l] contains l vectors which decribe the original 
%          d-dimensional feature space.
%  m [1 x 1] is dimension of the reduced feature space which has 
%          to be less or equal to min(N,K).
%  method [string] method of eigenvalue decomposition,
%     'default' for eig(cov(X')), 'ecov' for ecov(X).
%
% Output:
%  T [m x d] is the transformation matrix.
%  sumeigv [1 x 1] is the error of used transformation, which is 
%          equal to the value of the minimized objective fuction.
%  eigv [d x 1] contains sorted eigenvalues.
%
% See KENELPCA.
%

% Statistical Pattern Recognition Toolbox, Vojtech Franc, Vaclav Hlavac
% (c) Czech Technical University Prague, http://cmp.felk.cvut.cz
% Written Vojtech Franc (diploma thesis) 19.06.00
% Modifications
% 21-may-2001, V.Franc, ecov method added
% 21-dec-2000

l=size(X,2);

if nargin < 2, 
   m = size(X,1);
end

if nargin < 3 | strcmpi( method, 'default') == 1,

   [V,D]=eig(cov(X'));
   [eigv,inxDesc]=sort(-diag(D));
   eigv=-eigv;
   T=V(:,inxDesc);
else
  [V,eigv] = ecov( X );
  
  if m > length( eigv ),
    disp('Desired data dimension is too big.');
    T = V;
  end
end

sumeigv=sum(eigv(m+1:end));

T = V(:,1:m)';

return;