function?[P_XP_XtD]=EM_KPCA（XXtn_pctypepar1par2）

????%?Threshold?for?norm?difference?in?E-M
????Epsilon?=?0.005;

????%%%?Expectation?Maximization?Kernel?Principal?Component?Analysis
????%%%
????%%%?Inputs??
????%?????X??:?training?data?points??（number?of?samples??x?dimension）
????%?????Xt?:?testing??data?points??（number?of?samples??x?dimension）
????%
????%?????n_pc?:?number?of?principal?componets?onto?which?data?are?projected?
????%
????%??????????????????????????????????????????????????????par1????par2?
????%?????type:??‘G‘?Gaussian???Kernel??exp（（|x-y|^2）/w）???w???????0?
????%????????????‘P‘?Polynomial?Kernel??（+c）^a:???????a???????c?????
????%
????%%??Output?
????%?????P_X??:?projection?of?training?data??onto?the?first?n_pc??principal?componets?（number?of?samples??x?n_pc）
????%?????P_Xt?:?projection?of?testing??data??onto?the?first?n_pc??principal?componets?（number?of?samples??x?n_pc）
????%????????
????%?????D????:?eigenvalues?of?the?centralized?（cen_K）?training?data?kernel?matrix?
????%??????????:?!!!!??eigenvalues?coresponding?to?the?sample?covariance?matrix?are?sqrt（D）/（n-1）

???????
????[ndim]=size（X）;
????[ntdim]=size（Xt）;

????%%%?training?data?kernel?matrix?construction??
????K=Kernel（Xtypepar1par2）;
????
????%%%?centering?of?K?
????M=eye（n）-ones（nn）/n;
????cen_K=M*K*M;
????

????%%%?EM-KPCA?
????%%%?in?contrast?to?the?NC?paper?there?is?a?change?in?notation?:?X?<-->?Y
????

????Gamma=randn（nn_pc）;?%%%?random?intialization?

????iter=1;
????err（1）=Epsilon+1;?
????????
????while?err（iter）?>??Epsilon?????
??????%?iter??
??????%%%%%?E-step?
??????LC=Gamma‘*cen_K;
??????Y=inv（LC*Gamma）*LC;

??????%%%%%?M-step?
??????Gamma_old=Gamma;

??????Gamma=Y‘*inv（Y*Y‘）;?
??????
??????iter=iter+1;???
??????err（iter）=norm（Gamma_old-Gamma）;
??????

????end?
????
????
????%%%?getting?eigenvalues?

????ort_Gamma=orth（Gamma）;
????Y=cen_K*ort_Gamma;
????[VD]=eig（cov（Y））;
????[Dind]=sort（diag（D）*（n-1））;
????D=flipud（D）;
????ind=flipud（ind）;
???
????V=V（:ind）;?????????????%%%?sorting??eigenvectors??
????YV=Y*V;?????????????????%%%?rotation?to?Kernel?PCA??
?
????%%%?training?data?projection

????P_X=YV;
????????
????%%%?TESTING?PART?
????
????%?testing?data?kernel?matrix?construction?
????Kt=Kernel_Test（XXttypepar1par2）;
????
????%%%?centering?of?Kt?
????Mt=ones（ntn）/n;
????cen_Kt?=?（Kt?-?Mt*K）*M;

????????
????%%%?testing??data?projection?
????P_Xt=cen_Kt*ort_Gamma*V;
????

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

?????文件???????1449??2003-04-21?18:07??PLS_SIMPLS.m

?????文件???????2430??2003-04-21?18:07??EM_KPCA.m

?????文件???????5465??2003-04-23?16:10??example.m

?????文件????????851??2003-04-21?18:07??Kernel.m

?????文件????????922??2003-05-22?21:13??Kernel_Test.m

?????文件???????1534??2003-04-21?18:07??KerNIPALS.m

?????文件???????1575??2003-04-21?18:07??KerPLS_eig.m

?????文件???????1122??2003-04-21?18:07??KerSIMPLS1.m

?????文件???????1216??2003-04-23?16:10??KerSIMPLS.m

?????文件????????813??2003-04-21?18:07??KerSIMPLS_Test.m

?????文件???????2154??2003-04-21?18:07??KPCA.m

?????文件???????1165??2003-04-21?18:07??KPCR.m

?????文件???????1084??2003-04-21?18:07??KPCR_cent.m

?????文件???????1521??2003-04-21?18:07??KRR_cent.m

?????文件???????1228??2003-04-21?18:07??PCR_cent.m

?????文件????????624??2003-04-21?18:07??PLS_SB.m

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

????????????????25153????????????????????16