function?demo1
%
%?Encoding?and?retrieval?of?motion?in?a?latent?space?of?reduced?dimensionality.
%?This?source?code?is?the?implementation?of?the?algorithms?described?in?
%?Section?2.7.1?p.55?of?the?book?“Robot?Programming?by?Demonstration:?A?
%?Probabilistic?Approach“.?
%
%?Author:	Sylvain?Calinon?2009
%			http://programming-by-demonstration.org
%
%?This?program?loads?a?dataset?finds?a?latent?space?of?lower?dimensionality
%?encapsulating?the?important?characteristics?of?thge?motion?using?
%?Principal?Component?Analysis?（PCA）?trains?a?Gaussian?Mixture?Model?（GMM）?
%?using?the?data?projected?in?this?latent?space?re-projects?the?Gaussian?
%?in?the?original?data?space?and?plots?the?result.?Training?a?GMM?with?
%?EM?algorithm?usually?fails?to?find?a?good?local?optimum?when?data?are
%?high-dimensional.?By?projecting?the?original?dataset?in?a?latent?space?
%?as?a?pre-processing?step?GMM?training?can?be?performed?in?a?robust?way
%?and?the?Gaussian?parameters?can?be?projected?back?to?the?orginal?data
%?space.
%
%?This?source?code?is?given?for?free!?However?I?would?be?grateful?if?you?refer?
%?to?the?book?（or?corresponding?article）?in?any?academic?publication?that?uses?
%?this?code?or?part?of?it.?Here?are?the?corresponding?BibTex?references:?
%
%?@book{Calinon09book
%???author=“S.?Calinon“
%???title=“Robot?Programming?by?Demonstration:?A?Probabilistic?Approach“
%???publisher=“EPFL/CRC?Press“
%???year=“2009“
%???note=“EPFL?Press?ISBN?978-2-940222-31-5?CRC?Press?ISBN?978-1-4398-0867-2“
%?}
%
%?@article{Calinon07
%???title=“On?Learning?Representing?and?Generalizing?a?Task?in?a?Humanoid?Robot“
%???author=“S.?Calinon?and?F.?Guenter?and?A.?Billard“
%???journal=“IEEE?Transactions?on?Systems?Man?and?Cybernetics?Part?B“
%???year=“2007“
%???volume=“37“
%???number=“2“
%???pages=“286--298“
%?}

%%?Definition?of?the?number?of?components?used?in?GMM?and?the?number?of?
%%?principal?components.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
nbStates?=?3;
nbPC?=?2;

%%?Load?a?dataset?consisting?of?3?demonstrations?of?a?4D?signal?
%%?（3D?spatial?components?+?1D?temporal?component）.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
load（‘data/data.mat‘）;
[nbVarnbData]?=?size（Data）;

%%?Projection?of?the?data?in?a?latent?space?using?PCA.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Re-center?the?data
Data_mean?=?repmat（mean（Data（2:end:）2）?1?nbData）;
centeredData?=?Data（2:end:）?-?Data_mean;
%Extract?the?eigencomponents?of?the?covariance?matrix?
[Ev]?=?eig（cov（centeredData‘））;
E?=?fliplr（E）;
%Compute?the?transformation?matrix?by?keeping?the?first?nbPC?eigenvectors
A?=?E（:1:nbPC）;
%Project?the?data?in?the?latent?space
nbVar2?=?nbPC+1;
Data2（1:）?=?Data（1:）;
Data2（2:nbVar2:）?=?A‘?*?centeredData;


%%?Training?of?GMM?by?EM?algorithm?initialized?by?k-means?clustering.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2009-04-03?15:32??GMM-latentSpace-v2.0\
?????目錄???????????0??2009-04-03?15:32??GMM-latentSpace-v2.0\data\
?????文件????????7984??2006-09-17?04:06??GMM-latentSpace-v2.0\data\data.mat
?????文件??????102820??2008-10-15?05:59??GMM-latentSpace-v2.0\data\GMM-latentSpace-graph01.eps
?????文件????????4806??2009-07-22?13:54??GMM-latentSpace-v2.0\demo1.m
?????文件????????5553??2009-07-22?13:29??GMM-latentSpace-v2.0\EM.m
?????文件????????1645??2009-07-22?13:25??GMM-latentSpace-v2.0\EM_init_kmeans.m
?????文件?????????958??2009-07-22?13:25??GMM-latentSpace-v2.0\gaussPDF.m
?????文件????????1985??2009-07-22?13:35??GMM-latentSpace-v2.0\plotGMM.m