function??[eigvector?eigvalue?meandatanew_dim]?=?pca2drow（Xoptions）
%?PCA2dd??2D?row??Principal?Component?Analysis.
%
%?Synopsis:
%??model?=?pca2dd（X）
%??model?=?pca2dd（Xnew_dim）
%??model?=?pca2dd（Xvar）
%
%?Description:
%??It?computes?2D?row?Principal?Component?Analysis
%
%??model?=?pca2dd（Xnew_dim）?use?to?specify?explicitely?output
%???dimension?where?new_dim?>=?1.
%
%??model?=?pca2dd（Xvar）?use?to?specify?a?portion?of?discarded
%???variance?in?data?where?0?<=?var?%???selected?be?as?small?as?possbile?and?to?satisfy?
%?????var?>=?MsErr（new_dim）/MaxMsErr?
%???
%???where?MaxMsErr?=?sum（sum（X.^2））.?
%
%?Input:
%??X[xaxanumtr]?training?data?xa--rowxa--ranknumtr--train?num
%
%??new_dim?[1x1]?Output?dimension;?new_dim?>?1?（default?new_dim?=?dim）;
%??var?[1x1]?Portion?of?discarded?variance?in?data.
%
%?Ouputs:
%??model?[struct]?Linear?projection:
%???.W?[dim?x?new_dim]?Projection?matrix.
%???.b?[new_dim?x?1]?Bias.
%??
%???.eigval?[dim?x?1]?eigenvalues.
%???.mse?[real]?Mean?square?representation?error.
%???.MsErr?[dim?x?1]?Mean-square?errors?with?respect?to?number?
%?????of?basis?vectors;?mse=MsErr（new_dim）.
%???.mean_X?[dim?x?1]?mean?of?training?data.
%
%%

%?get?dimensions
[xa~numtr]=size（X）;

%?process?input?arguments
if?nargin?????options.PCARatio?=?0.99;
end

%?centering?data
meandata?=?mean（X3）;
X=X-repmat（meandata[1?1?numtr]）;

%?covariance
Gt?=?zeros（xaxa）;
for?j=1:numtr
????Gt?=?Gt?+?X（:?:?j）*X（:?:?j）‘/numtr;
end

%?eigenvalue?decomposition
[VD]=eig（Gt）;
[eigvalueindexv]=sort（-diag（D））;
sortV=?V（:indexv）;

%?decide?about?the?new_dimension
if?options.PCARatio?>=?1
??new_dim?=?options.PCARatio;???%?new_dim?enterd?explicitely
else
?new_dim=options.PCARatio*numtr;
end

%?take?new_dim?most?important?eigenvectors
eigvector=sortV（:1:new_dim）;

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2014-11-10?20:09??2DPCA\
?????文件????????1829??2013-10-08?21:52??2DPCA\2DPCA_knn.asv
?????文件?????2914492??2013-10-08?16:27??2DPCA\AR2D_data.mat
?????文件?????3729559??2013-10-08?16:25??2DPCA\ORL2D_data.mat
?????文件????????2145??2013-10-11?18:44??2DPCA\PCA2D_knn.asv
?????文件????????2220??2014-11-10?20:08??2DPCA\PCA2D_knn.m
?????文件?????1396287??2013-10-08?16:15??2DPCA\Yale2D_data.mat
?????文件????????1806??2013-10-08?19:58??2DPCA\pca2dd.asv
?????文件????????1817??2013-10-08?21:44??2DPCA\pca2dr.asv
?????文件????????1819??2013-10-08?21:54??2DPCA\pca2drow.m