somtoolbox2/pcaproj.m
4dbef185
 function [P,V,me,l] = pcaproj(D,arg1,arg2)
 
 %PCAPROJ Projects data vectors using Principal Component Analysis.
 %
 % [P,V,me,l] = pcaproj(D, odim)
 % P =          pcaproj(D, V, me)
 %
 %  Input and output arguments ([]'s are optional)
 %   D      (matrix) size dlen x dim, the data matrix
 %          (struct) data or map struct            
 %   odim   (scalar) how many principal vectors are used
 %  
 %   P      (matrix) size dlen x odim, the projections
 %   V      (matrix) size dim x odim, principal eigenvectors (unit length)
 %   me     (vector) size 1 x dim, center point of D
 %   l      (vector) size 1 x odim, the corresponding eigenvalues, 
 %                   relative to total sum of eigenvalues
 %                   
 % See also SAMMON, CCA.
 
 % Contributed to SOM Toolbox 2.0, February 2nd, 2000 by Juha Vesanto
 % Copyright (c) by Juha Vesanto
 % http://www.cis.hut.fi/projects/somtoolbox/
 
 % juuso 191297 070200
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 error(nargchk(2, 3, nargin)); % check the number of input arguments
 
 % the data
 if isstruct(D), 
   if strcmp(D.type,'som_map'), D=D.codebook; else D=D.data; end
 end
 [dlen dim] = size(D);
 
 if nargin==2, 
 
   odim = arg1;
     
   % autocorrelation matrix
   A = zeros(dim);
   me = zeros(1,dim);
   for i=1:dim, 
     me(i) = mean(D(isfinite(D(:,i)),i)); 
     D(:,i) = D(:,i) - me(i); 
   end  
   for i=1:dim, 
     for j=i:dim, 
       c = D(:,i).*D(:,j); c = c(isfinite(c));
       A(i,j) = sum(c)/length(c); A(j,i) = A(i,j); 
     end
   end
   
   % eigenvectors, sort them according to eigenvalues, and normalize
   [V,S]   = eig(A);
   eigval  = diag(S);
   [y,ind] = sort(abs(eigval)); 
   eigval  = eigval(flipud(ind));
   V       = V(:,flipud(ind)); 
   for i=1:odim, V(:,i) = (V(:,i) / norm(V(:,i))); end
   
   % take only odim first eigenvectors
   V = V(:,1:odim);
   l = abs(eigval)/sum(abs(eigval));
   l = l(1:odim); 
 
 else % nargin==3, 
 
   V = arg1;
   me = arg2;
   odim = size(V,2);    
   D = D-me(ones(dlen,1),:);
   
 end
   
 % project the data using odim first eigenvectors
 P = D*V;
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%