function demo_GMM02
% GMM with different covariance structures.
%
% Writing code takes time. Polishing it and making it available to others takes longer!
% If some parts of the code were useful for your research of for a better understanding
% of the algorithms, please reward the authors by citing the related publications,
% and consider making your own research available in this way.
%
% @article{Calinon16JIST,
% author="Calinon, S.",
% title="A Tutorial on Task-Parameterized Movement Learning and Retrieval",
% journal="Intelligent Service Robotics",
% publisher="Springer Berlin Heidelberg",
% doi="10.1007/s11370-015-0187-9",
% year="2016",
% volume="9",
% number="1",
% pages="1--29"
% }
%
% Copyright (c) 2015 Idiap Research Institute, http://idiap.ch/
% Written by Sylvain Calinon, http://calinon.ch/
%
% This file is part of PbDlib, http://www.idiap.ch/software/pbdlib/
%
% PbDlib is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License version 3 as
% published by the Free Software Foundation.
%
% PbDlib is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with PbDlib. If not, see .
addpath('./m_fcts/');
%% Parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
model.nbStates = 5; %Number of states in the GMM
model.nbVar = 2; %Number of variables [x1,x2]
nbData = 100; %Length of each trajectory
nbSamples = 5; %Number of demonstrations
%Parameters of the EM algorithm
nbMinSteps = 50; %Minimum number of iterations allowed
nbMaxSteps = 200; %Maximum number of iterations allowed
maxDiffLL = 1E-5; %Likelihood increase threshold to stop the algorithm
diagRegularizationFactor = 1E-2; %Regularization term is optional
%% Load handwriting data
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
demos=[];
load('data/2Dletters/C.mat');
Data=[];
a=pi/3;
R = [cos(a) sin(a); -sin(a) cos(a)];
for n=1:nbSamples
s(n).Data = spline(1:size(demos{n}.pos,2), demos{n}.pos, linspace(1,size(demos{n}.pos,2),nbData)); %Resampling
Data = [Data, R*s(n).Data];
end
%Initialization
%model = init_GMM_kmeans(Data, model);
model = init_GMM_timeBased([repmat(1:nbData,1,nbSamples); Data], model);
model.Mu = model.Mu(2:end,:);
model.Sigma = model.Sigma(2:end,2:end,:);
nbData = nbData * nbSamples;
%% EM with isotropic covariances
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for nbIter=1:nbMaxSteps
fprintf('.');
%E-step
[L, GAMMA] = computeGamma(Data, model); %See 'computeGamma' function below
GAMMA2 = GAMMA ./ repmat(sum(GAMMA,2),1,nbData);
%M-step
for i=1:model.nbStates
%Update Priors
model.Priors(i) = sum(GAMMA(i,:)) / nbData;
%Update Mu
model.Mu(:,i) = Data * GAMMA2(i,:)';
%Update Sigma
DataTmp = Data - repmat(model.Mu(:,i),1,nbData);
model.Sigma(:,:,i) = diag(diag(DataTmp * diag(GAMMA2(i,:)) * DataTmp')) + eye(size(Data,1)) * diagRegularizationFactor;
end
model.Sigma = repmat(eye(model.nbVar),[1 1 model.nbStates]) * mean(mean(mean(model.Sigma)));
%Compute average log-likelihood
LL(nbIter) = sum(log(sum(L,1))) / nbData;
%Stop the algorithm if EM converged (small change of LL)
if nbIter>nbMinSteps
if LL(nbIter)-LL(nbIter-1)nbMinSteps
if LL(nbIter)-LL(nbIter-1)nbMinSteps
if LL(nbIter)-LL(nbIter-1)