function?demo1
%
%?Demo?of?Gaussian?Mixture?Regression?（GMR）.?
%?This?source?code?is?the?implementation?of?the?algorithms?described?in?
%?Section?2.4?p.38?of?the?book?“Robot?Programming?by?Demonstration:?A?
%?Probabilistic?Approach“.?
%
%?Author:	Sylvain?Calinon?2009
%			http://programming-by-demonstration.org
%
%?The?program?loads?a?3D?dataset?trains?a?Gaussian?Mixture?Model?
%?（GMM）?and?retrieves?a?generalized?version?of?the?dataset?with?associated?
%?constraints?through?Gaussian?Mixture?Regression?（GMR）.?Each?datapoint?
%?has?3?dimensions?consisting?of?1?temporal?value?and?2?spatial?values?
%?（e.g.?drawing?on?a?2D?Cartesian?plane）.?A?sequence?of?temporal?values?is?
%?used?as?query?points?to?retrieve?a?sequence?of?expected?spatial?
%?distributiuon?through?Gaussian?Mixture?Regression?（GMR）.
%
%?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.??GMM中使用的組件數量的定義
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
nbStates?=?4;

%%?Load?a?dataset?consisting?of?3?demonstrations?of?a?2D?signal.?加載由3個2D信號演示組成的數據集
load（‘data/data1.mat‘）;?%load?‘Data‘
nbVar?=?size（Data1）;

%%?Training?of?GMM?by?EM?algorithm?initialized?by?k-means?clustering.??通過EM算法對GMM進行訓練，通過k均值聚類進行初始化。
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[Priors?Mu?Sigma]?=?EM_init_kmeans（Data?nbStates）;
[Priors?Mu?Sigma]?=?EM（Data?Priors?Mu?Sigma）;

%%?Use?of?GMR?to?retrieve?a?generalized?version?of?the?data?and?associated?使用GMR檢索數據和相關約束的通用版本。?一系列時間值用作輸入，并檢索期望的分布。
%%?constraints.?A?sequence?of?temporal?values?is?used?as?input?and?the?
%%?expected?distribution?is?retrieved.?
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
expData（1:）?=?linspace（min（Data（1:））?max（Data（1:））?100）;
[expData（2:nbVar:）?expSigma]?=?GMR（Priors?Mu?Sigma??expData（1:）?[1]?[2:nbVar]）;

%%?Plot?of?the?data?數據圖
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure（‘position‘[10101000800]‘name‘‘GMM-GMR-demo1‘）;
%plot?1D
for?n=1:nbVar-1
??subplot（3*（nbVar-1）2（n-1）*2+1）;?hold?on;
??plot（Data（1:）?Data（n+1:）?‘x‘?‘markerSize‘?4?‘

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2018-03-22?13:41??GMM\
?????目錄???????????0??2018-03-22?19:48??GMM\GMM-GMR-v2.0\
?????目錄???????????0??2009-04-03?15:32??GMM\GMM-GMR-v2.0\data\
?????文件????????7384??2008-04-18?10:26??GMM\GMM-GMR-v2.0\data\data1.mat
?????文件????????9784??2008-04-18?10:26??GMM\GMM-GMR-v2.0\data\data2_a.mat
?????文件????????1800??2008-04-18?10:26??GMM\GMM-GMR-v2.0\data\data2_b.mat
?????文件????????7392??2008-04-18?10:27??GMM\GMM-GMR-v2.0\data\data3_a.mat
?????文件????????7392??2008-04-18?10:27??GMM\GMM-GMR-v2.0\data\data3_b.mat
?????文件????????4986??2018-03-21?11:45??GMM\GMM-GMR-v2.0\demo1.m
?????文件????????4469??2009-07-22?13:29??GMM\GMM-GMR-v2.0\demo2.m
?????文件????????6157??2009-07-22?13:28??GMM\GMM-GMR-v2.0\demo3.m
?????文件????????5553??2009-07-22?13:29??GMM\GMM-GMR-v2.0\EM.m
?????文件????????1645??2009-07-22?13:25??GMM\GMM-GMR-v2.0\EM_init_kmeans.m
?????文件?????????958??2009-07-22?13:25??GMM\GMM-GMR-v2.0\gaussPDF.m
?????文件????????5374??2018-03-22?19:48??GMM\GMM-GMR-v2.0\GMR.m
?????文件????????1985??2009-07-22?13:35??GMM\GMM-GMR-v2.0\plotGMM.m
?????目錄???????????0??2014-06-18?19:23??GMM\task-parameterized-tensor-GMM-with-LQR\
?????目錄???????????0??2014-02-11?22:42??GMM\task-parameterized-tensor-GMM-with-LQR\data\
?????文件???????43247??2014-02-02?23:33??GMM\task-parameterized-tensor-GMM-with-LQR\data\DataLQR01.mat
?????文件????????8715??2014-06-18?19:24??GMM\task-parameterized-tensor-GMM-with-LQR\demo01.m
?????文件????????2328??2014-06-18?15:01??GMM\task-parameterized-tensor-GMM-with-LQR\demo_testLQR01.m
?????文件????????2537??2014-06-18?15:01??GMM\task-parameterized-tensor-GMM-with-LQR\demo_testLQR02.m
?????文件????????3113??2014-06-18?19:23??GMM\task-parameterized-tensor-GMM-with-LQR\EM_tensorGMM.m
?????文件????????2163??2014-06-18?15:02??GMM\task-parameterized-tensor-GMM-with-LQR\estimateAttractorPath.m
?????文件?????????877??2014-02-02?20:58??GMM\task-parameterized-tensor-GMM-with-LQR\gaussPDF.m
?????文件????????1123??2014-02-02?21:01??GMM\task-parameterized-tensor-GMM-with-LQR\init_tensorGMM_timebased.m
?????文件?????????938??2014-02-02?22:34??GMM\task-parameterized-tensor-GMM-with-LQR\plotGMM.m
?????文件????????1907??2014-06-18?20:45??GMM\task-parameterized-tensor-GMM-with-LQR\readme.txt
?????文件????????1384??2014-06-18?17:47??GMM\task-parameterized-tensor-GMM-with-LQR\reproduction_DS.m
?????文件????????3189??2014-06-18?15:02??GMM\task-parameterized-tensor-GMM-with-LQR\reproduction_LQR_finiteHorizon.m
?????文件????????2149??2014-06-18?15:01??GMM\task-parameterized-tensor-GMM-with-LQR\reproduction_LQR_infiniteHorizon.m
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