function?r=LFDA（XYrmetrickNN）
%
%?Local?Fisher?Discriminant?Analysis?for?Supervised?Dimensionality?Reduction
%
%?Usage:
%???????[TZ]=LFDA（XYrmetric）
%
%?Input:
%????X:??????d?x?n?matrix?of?original?samples
%????????????d?---?dimensionality?of?original?samples
%????????????n?---?the?number?of?samples?
%????Y:??????n?dimensional?vector?of?class?labels
%????r:??????dimensionality?of?reduced?space?（default:?d）
%????metric:?type?of?metric?in?the?embedding?space?（default:?‘weighted‘）
%????????????‘weighted‘????????---?weighted?eigenvectors?
%????????????‘orthonormalized‘?---?orthonormalized
%????????????‘plain‘???????????---?raw?eigenvectors
%????kNN:????parameter?used?in?local?scaling?method?（default:?7）
%
%?Output:
%????T:?d?x?r?transformation?matrix?（Z=T‘*X）
%????Z:?r?x?n?matrix?of?dimensionality?reduced?samples?
%
%?（c）?Masashi?Sugiyama?Department?of?Compter?Science?Tokyo?Institute?of?Technology?Japan.
%?????sugi@cs.titech.ac.jp?????http://sugiyama-www.cs.titech.ac.jp/~sugi/software/LFDA/

if?nargin<2
??error（‘Not?enough?input?arguments.‘）
end
[d?n]=size（X）;

if?nargin<3
??r=d;
end

if?nargin<4
??metric=‘weighted‘;
end

if?nargin<5
??kNN=17;
end

tSb=zeros（dd）;
tSw=zeros（dd）;

for?c=unique（Y）
??Xc=X（:Y==c）;
??nc=size（Xc2）;

??%?Define?classwise?affinity?matrix
??Xc2=sum（Xc.^21）;
??distance2=repmat（Xc2nc1）+repmat（Xc2‘1nc）-2*Xc‘*Xc;
??[sortedindex]=sort（distance2）;
??kNNdist2=sorted（kNN+1:）;
??sigma=sqrt（kNNdist2）;
??localscale=sigma‘*sigma;
??flag=（localscale~=0）;
??A=zeros（ncnc）;
??A（flag）=exp（-distance2（flag）./localscale（flag））;

??Xc1=sum（Xc2）;
??G=Xc*（repmat（sum（A2）[1?d]）.*Xc‘）-Xc*A*Xc‘;
??tSb=tSb+G/n+Xc*Xc‘*（1-nc/n）+Xc1*Xc1‘/n;
??tSw=tSw+G/nc;
end

X1=sum（X2）;
tSb=tSb-X1*X1‘/n-tSw;

tSb=（tSb+tSb‘）/2;
tSw=（tSw+tSw‘）/2;

aer=sum（tSb）;
ber=sum（tSw）;
r=aer./ber;
r=r./20;

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

?????文件???????1907??2015-04-02?20:08??LFDA.m

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

?????????????????1907????????????????????1