diff toolboxes/FullBNT-1.0.7/bnt/examples/static/Zoubin/ffa.m @ 0:e9a9cd732c1e tip

first hg version after svn

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolboxes/FullBNT-1.0.7/bnt/examples/static/Zoubin/ffa.m	Tue Feb 10 15:05:51 2015 +0000
@@ -0,0 +1,75 @@
+% function [L,Ph,LL]=ffa(X,K,cyc,tol);
+% 
+% Fast Maximum Likelihood Factor Analysis using EM
+%
+% X - data matrix
+% K - number of factors
+% cyc - maximum number of cycles of EM (default 100)
+% tol - termination tolerance (prop change in likelihood) (default 0.0001)
+%
+% L - factor loadings 
+% Ph - diagonal uniquenesses matrix
+% LL - log likelihood curve
+%
+% Iterates until a proportional change < tol in the log likelihood 
+% or cyc steps of EM 
+%
+
+function [L,Ph,LL]=ffa(X,K,cyc,tol);
+
+if nargin<4  tol=0.0001; end;
+if nargin<3  cyc=100; end;
+
+N=length(X(:,1));
+D=length(X(1,:));
+tiny=exp(-700);
+
+X=X-ones(N,1)*mean(X);
+XX=X'*X/N;
+diagXX=diag(XX);
+
+randn('seed', 0);
+cX=cov(X);
+scale=det(cX)^(1/D);
+L=randn(D,K)*sqrt(scale/K);
+Ph=diag(cX);
+
+I=eye(K);
+
+lik=0; LL=[];
+
+const=-D/2*log(2*pi);
+
+
+for i=1:cyc;
+
+  %%%% E Step %%%%
+  Phd=diag(1./Ph);
+  LP=Phd*L;
+  MM=Phd-LP*inv(I+L'*LP)*LP';
+  dM=sqrt(det(MM));
+  beta=L'*MM;
+  XXbeta=XX*beta';
+  EZZ=I-beta*L +beta*XXbeta;
+
+  %%%% Compute log likelihood %%%%
+  
+  oldlik=lik;
+  lik=N*const+N*log(dM)-0.5*N*sum(diag(MM*XX));
+  fprintf('cycle %i lik %g \n',i,lik);
+  LL=[LL lik];
+  
+  %%%% M Step %%%%
+
+  L=XXbeta*inv(EZZ);
+  Ph=diagXX-diag(L*XXbeta');
+
+  if (i<=2)    
+    likbase=lik;
+  elseif (lik<oldlik)     
+    disp('VIOLATION');
+  elseif ((lik-likbase)<(1+tol)*(oldlik-likbase)||~isfinite(lik))  
+    break;
+  end;
+
+end