%**********************************************
%?Aim?:?The?first?AI?program?homework
%?title?:?PCA?for?face?recognition
%?Author?:?GongWanlu?&?Hufei
%?Version?:?1.0?final
%?Submit?Time?:?2011-04-07
%**********************************************

%?%%%%%%%%%%%%%%%%%%%%%%INITIAL
clear?all
clc
close?all

%?%%%%%%%%%%%%%%%%%%%%%%Some?variables?according?to?the?Yale?Face?DB
Num_subject?=?15;
Num_image?=?11;
Train_num_image?=?8;????????????????????%for?every?subject?we?choose?8?to?train
Test_num_image?=?9;?????????????????????%choose?the?left?3?images?to?test

%?%%%%%%%%%%%%%%%%%%%%%%Load?Data
Data?=?[];
for?i=1:Num_subject
????for?j=1:Train_num_image
????????path?=?sprintf（‘FaceDB_yaleA/%03d/%02d.jpg‘ij）;
????????pic?=?imread?（path）;????????????%read?one?picture
????????
????????%Make?Data?Add?pic?into?Data
????????pic_line?=?pic（1:147*137）;??????%The?pic?size?is?147*137
????????????????????????????????????????%pic_line?is?1*N?N=147*137.?from?up?to
????????????????????????????????????????%downleft?to?right.
????????????????????????????????????????%Reshape?2D?image?to?1D?image
????????????????????????????????????????%vectors
????????Data?=?[Data;double（pic_line）];?%add?pic_line?into?Data
????end
end
%?End?of?Load?Data

%%%%%%%%%%%%%%%%%%%%%%%Substract?mean?from?Data?and?make?covariance?from?centering?Data
samplemean?=?mean（Data）;????????????????%mean?pic?1*N

for?k?=?1:（Num_subject?*?Train_num_image）
????xmean（k:）=Data（k:）-samplemean;????%Normalize
end?????????????????????????????????????%xmean?is?M*N?each?line?is?one?pic
????????????????????????????????????????%data（mean?data）?be?normalized
sigma?=?xmean?*xmean‘;??????????????????%M*M??here?is?120*120
[V?D]=eig（sigma）;???????????????????????%calculate?the?eigenvalue&eigenvector
????????????????????????????????????????%eigenvalue?in?Dand?vectors?in?V
?D1=diag（D）;????????????????????????????%the?eigenvalues
?
?%%%%%%%%%%%%%%%%%%%%%%%%?Sorting?and?eliminating?eigenvalues
?%?At?first?:?sort?desc
?Dsort=flipud（D1）;
?Vsort=fliplr（V）;
?
?%choose?part?eigenvalues
?Dsum?=?sum（Dsort）;?????????????????????%sum?of?the?eigenvalueswe?only?choose?80%
????????????????????????????????????????%we?have?different?ways?to?choose
????????????????????????????????????????%eigenvalues?we?need90%or>1……
temp_sum?=?0;
p?=?0;
while（temp_sum/Dsum<0.8）
????p?=?p+1;
????temp_sum?=?sum（Dsort（1:p））;
end
%End?of?sort?part

?%%%%%%%%%%%%%%%%%%%%%%%Train?Step:?get?the?coordinate?system
?i=1;
?while（i<=p?&&?Dsort（i）>0）
?????face_base（:i）?=?Dsort（i）^（-1/2）?*?xmean‘?*?Vsort?（:i）;
?????i=i+1;
?end
?%?Dsort（i）^（-1/2）?used?to?normalize?make?variance=1
?%?face_base?is?N*p
?%?xmean‘?*?Vsort?（:i）;?is?change?small?matrix?to?big?matrix.?CHACHENG（Chinese）
?
?%next?sentence?is?vary?important?is?our?train?result
?allcoor?=?Data?*?face_base;
?%End?of?training
?
?%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Draw?part
??%draw?CDF
?x?=?Dsort?（1:p）;
?x?=?flipud?（x）;

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

?????文件???????4982??2011-04-08?00:32??PCA.m

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?????????????????4982????????????????????1