function?[test_targets?param_struct]?=?EM（train_patterns?train_targets?test_patterns?Ngaussians）

%?Classify?using?the?expectation-maximization?algorithm
%?Inputs:
%?	train_patterns	-?Train?patterns
%	train_targets	-?Train?targets
%???test_patterns???-?Test??patterns
%???Ngaussians??????-?Number?for?Gaussians?for?each?class?（vector）
%
%?Outputs
%	test_targets	-?Predicted?targets
%???param_struct????-?A?parameter?structure?containing?the?parameters?of?the?Gaussians?found

classes?????????????=?unique（train_targets）;?%Number?of?classes?in?targets
Nclasses????????????=?length（classes）;
Nalpha				=?Ngaussians;			?%Number?of?Gaussians?in?each?class
Dim?????????????????=?size（train_patterns1）;

max_iter???			=?100;
max_try?????????????=?5;
Pw					=?zeros（Nclassesmax（Ngaussians））;
sigma				=?zeros（Nclassesmax（Ngaussians）size（train_patterns1）size（train_patterns1））;
mu					=?zeros（Nclassesmax（Ngaussians）size（train_patterns1））;

%The?initial?guess?is?based?on?k-means?preprocessing.?If?it?does?not?converge?after
%max_iter?iterations?a?random?guess?is?used.
disp（‘Using?k-means?for?initial?guess‘）
for?i?=?1:Nclasses
????in??			=?find（train_targets==classes（i））;
????[initial_mu?targets?labels]	=?k_means（train_patterns（:in）train_targets（:in）Ngaussians（i））;
????for?j?=?1:Ngaussians（i）
????????gauss_labels????=?find（labels==j）;
????????Pw（ij）?????????=?length（gauss_labels）?/?length（labels）;
????????sigma（ij::）??=?diag（std（train_patterns（:in（gauss_labels））‘））;
????end
????mu（i1:Ngaussians（i）:）?=?initial_mu‘;
end

%Do?the?EM:?Estimate?mean?and?covariance?for?each?class?
for?c?=?1:Nclasses
????train	???=?find（train_targets?==?classes（c））;
????
????if?（Ngaussians（c）?==?1）
????????%If?there?is?only?one?Gaussian?there?is?no?need?to?do?a?whole?EM?procedure
????????sigma（c1::）??=?sqrtm（cov（train_patterns（:train）‘1））;
????????mu（c1:）???????=?mean（train_patterns（:train）‘）;
????else
????????
????????sigma_i?????????=?squeeze（sigma（c:::））;
????????old_sigma???????=?zeros（size（sigma_i））;?		%Used?for?the?stopping?criterion
????????iter			=?0;									%Iteration?counter
????????n			?	=?length（train）;					%Number?of?training?points
????????qi			????=?zeros（Nalpha（c）n）;	???	%This?will?hold?qi‘s
????????P				=?zeros（1Nalpha（c））;
????????Ntry????????????=?0;
????????
????????while?（（sum（sum（sum（abs（sigma_i-old_sigma））））?>?1e-4）?&?（Ntry?????????????old_sigma?=?sigma_i;
????????????
????????????%E?step:?Compute?Q（theta;?theta_i）
????????????for?t?=?1:n
????????????????data??=?train_patterns（:train（t））;
????????????????for?k?=?1:Nalpha（c）
????????????????????P（k）?=?Pw（ck）?*?p_single（data?squeeze（mu（ck:））?squeeze（sigma_i（k::）））;
????????????????end??????????
????????????????
????????????????for?i?=?1:Nalpha（c）
????????????????????qi（it）?=?P（i）?/?sum（P）;
????????????????end
????????????end
????????????
????????????%M?step:?theta_i+1?<-?argmax（Q（the

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件???????5336??2007-12-18?20:47??EM.m

?????文件???????1834??2003-06-26?21:14??k_means.m

-----------?---------??----------?-----??----

?????????????????7170????????????????????2