function?[Priors?Mu?Sigma]?=?EM_GMM（Data?nbStates?Stop_criterion）
%?Inputs?----------------------------------------------------------------------------------??
%???Data:?????D?x?N?array?representing?N?datapoints?of?D?dimensions.??
%???nbStates:?Number?K?of?GMM?components.??
%???Stop_criterion:?Stopping?criterion?1?or?2.
%?Outputs?---------------------------------------------------------------------------------??
%???Priors:???1?x?K?array?representing?the?prior?probabilities?of?the?K?GMM?components.???????????????
%???Mu:???????D?x?K?array?representing?the?centers?of?the?K?GMM?components.??
%???Sigma:????D?x?D?x?K?array?representing?the?covariance?matrices?of?the?K?GMM?components.??????????????
%------------------------------------------------------------------------------------------
%The?iteration?stop?condition?of?EM?
%EM?迭代停止條件
loglik_threshold?=?1e-10;
loglik_old?=?-realmax;
Epsilon?=?0.0001;
nbStep?=?0;
[nbVarnbData]?=?size（Data）;?%nbVar:The?dimensions?of?the?feature;;?nbData:The?number?of?points（samples）

%Initialization?parameter?based?on?k-means
%初始參數由k-means（其實也是一種特殊的高斯混合模型）決定
[Priors0?Mu0?Sigma0]?=?EM_init_kmeans（Data?nbStates）;??
Mu?=?Mu0;
Sigma?=?Sigma0;
Priors?=?Priors0;

while?（nbStep<1200）??
??nbStep?=?nbStep+1;?
??%?E-step------------------------------------------------???
??for?i=1:nbStates??
????%Compute?probability?p（x|i）??
????Pxi（:i）?=?gaussPDF（Data?Mu（:i）?Sigma（::i））;??
??end??
??%Compute?posterior?probability?p（i|x）??
??Pix_tmp?=?repmat（Priors[nbData?1]）.*Pxi;??
??Pix?=?Pix_tmp?./?（repmat（sum（Pix_tmp2）[1?nbStates]）+realmin）;
??%Compute?cumulated?posterior?probability??
??E?=?sum（Pix）;??
??
??%?M-step------------------------------------------------??
??for?i=1:nbStates??
????%Update?the?priors??
????Priors（i）?=?E（i）?/?nbData;??
????%Update?the?centers??
????Mu（:i）?=?Data*Pix（:i）?/?E（i）;??
????%Update?the?covariance?matrices??
????Data_tmp1?=?Data?-?repmat（Mu（:i）1nbData）;??
????Sigma（::i）?=?（repmat（Pix（:i）‘nbVar?1）?.*?Data_tmp1*Data_tmp1‘）?/?E（i）;??
????%?Add?a?tiny?variance?to?avoid?numerical?instability??
????Sigma（::i）?=?Sigma（::i）?+?1E-5.*diag（ones（nbVar1））;??
??end?
??
??if?Stop_criterion?==?1???????
??????%?Stopping?criterion?1
??????for?i=1:nbStates??
????????%Compute?the?new?probability?p（x|i）??
????????Pxi（:i）?=?gaussPDF（Data?Mu（:i）?Sigma（::i））;??
??????end??
??????%Compute?the?log?likelihood??
??????F?=?Pxi*Priors‘;??
??????F（find（F??????loglik?=?mean（log（F））;??
??????%Stop?the?process?depending?on?the?increase?of?the?log?likelihood???
??????if?abs（（loglik/loglik_old）-1）?????????break;??
??????end??
??????loglik_old?=?loglik;??
??elseif?Stop_criterion?==?2???????
??????%?Stopping?criterion?2
??????v?=?[sum（abs（Mu-Mu0））abs（Priors-Priors0）];
??????s?=?abs（Sigma-Sigma0）;
??????v2=0;
??????for?i?=?1:nbStates
??????????v2?=?v2?+?det（s（::i））;
??????end

??????if?（

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????3255??2016-03-25?15:10??EM_GMM.m
?????文件????????1588??2016-03-25?14:01??EM_init_kmeans.m
?????文件?????????738??2016-03-25?13:56??gaussPDF.m
?????文件??????537600??2012-03-30?14:55??GMM建模與EM算法.ppt
?????文件?????3585734??2016-03-25?15:24??MFCC_features.mat
?????文件??????217660??2012-03-29?19:01??高斯混合模型講解.pdf