function?rate?=?KPCA_SVM
%KPCA_SVM?Kernel?Principle?Component?Analysis?&?Support?Vector?Machine
%
%?Using?the?ORL?database?to?perform?a?face?recognition?method?
%?which?empolys?KPCA?as?features?extractor?and?LSVM?as?classifier?
%
%?Outputs????
%???Pattern???:?The?Pattern?of?the?test?data
%???rate??????:?The?recognition?rate
%?Inputs????
%???Train?????:?N?x?d?matrix?with?the?inputs?of?the?training?data?????
%???????????????N?is?the?number?of?training?points?d?is?the?dimension?of?data
%???Test??????:?N?x?d?matrix?with?the?inputs?of?the?test?data????????
%???????????????N?is?the?number?of?test?points?d?is?the?dimension
%???d?????????:?polynomial?degree
%???max_ev????:?Number?of?eigenvalues
%?

%?parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
load?S_train
Tr?=?S_train;
Tr_n?=?size（Tr?1）;
d?=?1;
max_ev?=?120;

%?test?set
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
load?S_test
Te?=?S_test;
Te_n?=?size（Te1）;

tic?%?set?clock?for?training
%?carry?out?Kernel?PCA
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%?compute?the?kernel?matrix?of?training?set
K_train?=?feval（‘poly_kernel‘Tr?Tr?d）;?
l?=?ones（Tr_nTr_n）/Tr_n;
K_train?=?K_train?-?l*K_train?-?K_train*l?+?l*K_train*l;??%?centering?in?feature?space

%?compute?eigenvectors?and?eigenvalues
[evecsevals]?=?eig（K_train/Tr_n）;?
[evalsind]?=?sort（diag（evals））;???%?diagonalize?and?sort?eigenvalues
Lambda?=?evals（end:-1:1）;
Ind?=?ind（end:-1:1）;

%?normalize?eigenvector?expansion?coefficients
for?i?=?1:max_ev
????Alpha（:?i）?=?evecs（:?Ind（i））/sqrt（Lambda（i）/Tr_n）;??
end
Train_Features?=?K_train?*?Alpha（:?1:max_ev）;???%?compute?features?of?training?set?

%?compute?kernel?matrix?of?test?set
K_test?=?feval（‘poly_kernel‘?Te?Tr?d）;???
ll?=?ones（Te_n?Tr_n）/Tr_n;
K_test?=?K_test?-?ll*K_train?-?K_test*l?+?ll*K_train*l;?%?centering?in?feature?space

Test_Features?=?K_test?*?Alpha（:?1:max_ev）;???%?extract?features

%?carry?out?LSVM?&?NN
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%?compute?Lagrange?multipliers?and?bias
for?i?=?1:40
????%?construct?training?targets
????Y（:?i）?=?ones（Tr_n?1）*（-1）;
????Y（5*i-4:5*i?i）?=?Y（5*i-4:5*i?i）*（-1）;??
????%?compute?coefficients?through?solving?quadratic?optimizaton?with?C=1e-8
????[alpha（:i）?B（:i）]?=?lsvctrain（Train_Features?Y（:?i）?1e-8）;?
end
toc??%?stop?watch?for?training

tic??%?set?watch?for?classification
%?construct?the?linear?test?matrix
d?=?2;
K_test_svm?=?feval（‘poly_kernel‘Test_Features?Train_Features?d）;??

%?mulitply?the?linear?matrix?
t?=?K_test_svm*alpha?.*?Y?+?repmat（B?Te_n?1）;

%?classify?with?decision?function
C?=?sign（t）;?%+?repmat（B?size（t1）?1））;

%?recognize?patterns?by?the?classifiers
Pattern?=?zeros（Te_n?1）;
for?i?=?1:Te_n
????Re?=find（C（i?:）?>?0?）;?%?find?the?classsifiers?with?output?‘1‘
????len（i）?=?length（Re）;

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

?????文件???????4130??2008-03-11?16:59??KPCA_SVM_Train\KPCA_SVM_Train.m

?????目錄??????????0??2008-09-18?09:53??KPCA_SVM_Train

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

?????????????????4130????????????????????2