echo on;clc;% This is a very basic demo of the mixture of factor analyzer software% written in Matlab by	Zoubin Ghahramani%			Dept of Computer Science%			University of Torontopause;		% Hit any key to continue % To demonstrate the software we generate a sample data set% from a mixture of two Gaussianspause;		% Hit any key to continue X1=randn(300,5);	% zero mean 5 dim Gaussian data X2=randn(200,5)+2;	% 5 dim Gaussian data with mean [1 1 1 1 1]X=[X1;X2];		% total 500 data points from mixture% Fitting the model is very easy. For example to fit a mixture of 2% factor analyzers with three factors each...pause;		% Hit any key to continue [Lh,Ph,Mu,Pi,LL]=mfa(X,2,3);% Lh, Ph, Mu, and Pi are the factor loadings, observervation% variances, observation means for each mixture, and mixing% proportions. LL is the vector of log likelihoods (the learning% curve). For more information type: help mfa% to plot the learning curve (log likelihood at each step of EM)...pause;		% Hit any key to continue plot(LL);% you get a more informative picture of convergence by looking at the% log of the first difference of the log likelihoods...pause;		% Hit any key to continue semilogy(diff(LL)); % you can look at some of the parameters of the fitted model... pause;		% Hit any key to continue MuPi% ...to see whether they make any sense given that me know how the% data was generated. % you can also evaluate the log likelihood of another data set under% the model we have just fitted using the mfa_cl (for Calculate% Likelihood) function. For example, here we generate a test from the% same distribution. X1=randn(300,5);X2=randn(200,5)+2;Xtest=[X1; X2];pause;		% Hit any key to continue mfa_cl(Xtest,Lh,Ph,Mu,Pi)% we should expect the log likelihood of the test set to be lower than% that of the training set.% finally, we can also fit a regular factor analyzer using the ffa% function (Fast Factor Analysis)...pause;		% Hit any key to continue [L,Ph,LL]=ffa(X,3);