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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 Toronto
pause; % Hit any key to continue
% To demonstrate the software we generate a sample data set
% from a mixture of two Gaussians
pause; % 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
Mu
Pi
% ...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);
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