New GMR example added

m_fcts/EM_GMM.m

@@ -2,7 +2,20 @@ function [model, GAMMA2, LL] = EM_GMM(Data, model)
 % Training of a Gaussian mixture model (GMM) with an expectation-maximization (EM) algorithm. 
 %
 % Author:	Sylvain Calinon, 2014
-%         http://programming-by-demonstration.org/SylvainCalinon
+%         http://programming-by-demonstration.org/lib/
+%
+% This source code is given for free! In exchange, please cite the following 
+% reference in any academic publication that uses this code or part of it:
+%
+% @article{Calinon07SMC,
+%   author="Calinon, S. and Guenter, F. and Billard, A. G.",
+%   title="On Learning, Representing and Generalizing a Task in a Humanoid Robot",
+%   journal="{IEEE} Trans. on Systems, Man and Cybernetics, Part {B}",
+%   year="2007",
+%   volume="37",
+%   number="2",
+%   pages="286--298",
+% }
 
 %Parameters of the EM algorithm
 nbMinSteps = 5; %Minimum number of iterations allowed

m_fcts/init_GMM_kmeans.m

 function model = init_GMM_kmeans(Data, model)
-%
 % This function initializes the parameters of a Gaussian Mixture Model 
 % (GMM) by using k-means clustering algorithm.
 %
@@ -12,16 +11,12 @@ function model = init_GMM_kmeans(Data, model)
 %   o Mu:       D x K array representing the centers of the K GMM components.
 %   o Sigma:    D x D x K array representing the covariance matrices of the 
 %               K GMM components.
-% Comments ---------------------------------------------------------------
-%   o This function uses the 'kmeans' function from the MATLAB Statistics 
-%     toolbox. If you are using a version of the 'netlab' toolbox that also
-%     uses a function named 'kmeans', please rename the netlab function to
-%     'kmeans_netlab.m' to avoid conflicts. 
 %
-% Copyright (c) 2006 Sylvain Calinon, LASA Lab, EPFL, CH-1015 Lausanne,
-%               Switzerland, http://lasa.epfl.ch
+% Author:	Sylvain Calinon, 2014
+%         http://programming-by-demonstration.org/lib/
 
-[nbVar, nbData] = size(Data);
+nbVar = size(Data,1);
+diagRegularizationFactor = 1E-2;
 
 [Data_id, model.Mu] = kmeansClustering(Data, model.nbStates);
 
@@ -30,7 +25,7 @@ for i=1:model.nbStates
   model.Priors(i) = length(idtmp);
   model.Sigma(:,:,i) = cov([Data(:,idtmp) Data(:,idtmp)]');
   %Regularization term to avoid numerical instability
-  model.Sigma(:,:,i) = model.Sigma(:,:,i) + eye(nbVar)*1E-2;
+  model.Sigma(:,:,i) = model.Sigma(:,:,i) + eye(nbVar)*diagRegularizationFactor;
 end
-model.Priors = model.Priors ./ sum(model.Priors);
+model.Priors = model.Priors / sum(model.Priors);
 

m_fcts/init_GMM_timeBased.m

 function model = init_GMM_timeBased(Data, model)
-%
 % This function initializes the parameters of a Gaussian Mixture Model 
 % (GMM) by using k-means clustering algorithm.
 %
@@ -12,17 +11,13 @@ function model = init_GMM_timeBased(Data, model)
 %   o Mu:       D x K array representing the centers of the K GMM components.
 %   o Sigma:    D x D x K array representing the covariance matrices of the 
 %               K GMM components.
-% Comments ---------------------------------------------------------------
-%   o This function uses the 'kmeans' function from the MATLAB Statistics 
-%     toolbox. If you are using a version of the 'netlab' toolbox that also
-%     uses a function named 'kmeans', please rename the netlab function to
-%     'kmeans_netlab.m' to avoid conflicts. 
 %
-% Copyright (c) 2006 Sylvain Calinon, LASA Lab, EPFL, CH-1015 Lausanne,
-%               Switzerland, http://lasa.epfl.ch
+% Author:	Sylvain Calinon, 2014
+%         http://programming-by-demonstration.org/lib/
 
-[nbVar, nbData] = size(Data);
+nbVar = size(Data,1);
 TimingSep = linspace(min(Data(1,:)), max(Data(1,:)), model.nbStates+1);
+diagRegularizationFactor = 1E-2;
 
 for i=1:model.nbStates
   idtmp = find( Data(1,:)>=TimingSep(i) & Data(1,:)<TimingSep(i+1));
@@ -30,7 +25,7 @@ for i=1:model.nbStates
   model.Mu(:,i) = mean(Data(:,idtmp)');
   model.Sigma(:,:,i) = cov(Data(:,idtmp)');
   %Regularization term to avoid numerical instability
-  model.Sigma(:,:,i) = model.Sigma(:,:,i) + eye(nbVar)*1E-2;
+  model.Sigma(:,:,i) = model.Sigma(:,:,i) + eye(nbVar)*diagRegularizationFactor;
 end
 model.Priors = model.Priors / sum(model.Priors);