function?[eigvector?eigvalue]?=?PCA_Bao（X?ReducedDimThd）
%PCA	Principal?Component?Analysis
%
%	Usage:
%???????[eigvector?eigvalue]?=?PCA（X?ReducedDim）
%???????[eigvector?eigvalue]?=?PCA（X）
%?
%?????????????Input:
%???????????????X???????-?Data?matrix.?Each?row?vector?of?fea?is?a?data?point.
%
%??????????ReducedDim???-?The?dimensionality?of?the?reduced?subspace.?If?0
%?????????????????????????all?the?dimensions?will?be?kept.?
%?????????????????????????Default?is?0.?
%
%?????????????Output:
%???????????????eigvector?-?Each?column?is?an?embedding?function?for?a?new
%???????????????????????????data?point?（row?vector）?x??y?=?x*eigvector
%???????????????????????????will?be?the?embedding?result?of?x.
%???????????????eigvalue??-?The?sorted?eigvalue?of?PCA?eigen-problem.?
%
%	Examples:
%?			fea?=?rand（710）;
%?			[eigvectoreigvalue]?=?PCA（fea4）;
%???????????Y?=?fea*eigvector;
%?
%?
P?=?X;
%??Calculate?the?mean?column?vector?of?the?matrix?P?and?substract
%??it?from?P?
row_P?=?size（P1）;
col_P?=?size（P2）;
PP=[];

???mean_P=?mean（P2）;
???temp=ones（1col_P）;
???PP?=?P-mean_P*temp;


%??Calculate?the?eigenvalues?and?eigenvectors?of?the?matrix?PP‘*PP?
Q=PP‘*PP;
[vector_Qvalue_Q]?=?eig（Q）;

%??Caculate?the??eigenvalues?and?eigenvectors?of?the?matrix?PP*PP‘
%??using?SVD（Singular?Value?Decomposition）
valuecov?=?value_Q;
vectcov?=?PP*vector_Q;
vectorcov?=?vectcov*value_Q^（-0.5）;


%??Sort?the?eigenvectors?and?the?eigenvalues?of?the?covariance?
%??matrix?of?P?with?the?decrease?of?the?eigenvalues?
????????eigvalue?=?diag（value_Q）;
????????[junk?index]?=?sort（-eigvalue）;
????????eigvalue?=?eigvalue（index）;
????????eigvector?=?vectorcov（:?index）;

%??Return?the?eigenvectors?and?the?eigenvalue?matrix?of?the?covariance
%??matrix?of?imgs
if?ReducedDim~=0
???if?ReducedDim>col_P
??????ReducedDim=col_P;
??????fprintf（‘Only?%d?vectors?exist...‘col_P）;
???end
???vectors?=?eigvector（:1:ReducedDim）;
???values?=?eigvalue（1:ReducedDim1:ReducedDim）;
else
????eigIdx?=?find（cumsum（eigvalue）./sum（eigvalue）?>=?Thd）;
????eigvalue?（eigIdx）?=?[];
????eigvector?（:eigIdx）?=?[];

end;

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

?????文件???????2175??2009-05-09?14:25??PCA.m

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

?????????????????2175????????????????????1