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##### RDA

Matlab code for reversible discriminant analysis (RDA).

##### Reference

Lan Bai, Yuan-Hai Shao*, Zhen Wang, Chun-Na Li. Reversible discriminant analysis[J]. Submitted. 2018

##### Main Function

[rX,W]= RDA(X,tY,g1,g2) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % RDA: % % [rX,W]= RDA(X,tY,g1,g2) % % Input: % X: Data matrix. (nolinear version is obtained by K(X,X)) % tY: labels of X % Parameters - % g1, g2: [0,inf) Paramter to tune the weight. % % Output: % rX: the data after dimensionality reduction. % W: mapping matrix % Examples: % X=rand(50,10); % tY = randint(50,1,[1,5]); % g1=1;g2=1;; % [rX,W]= RDA(X,tY,g1,g2) % % Version 1.1 --Jul/2018 % % Written by Zhen Wang (wangzhen@imu.edu.cn) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% t=max(tY); % number of classes [m,n]=size(X); %X=X-repmat(mean(X),m,1); //if needed, centralized A=zeros(n,n); % in-class discrimnant B=zeros(n,n); % between-class discrimnant for i=1:t Xt=X(tY==i,:); mt=size(Xt,1); tA=zeros(n,n); Mt=sum(Xt,1)/mt; % the mean of a class for j=1:mt tA=tA+(Xt(j,:)-Mt)'*(Xt(j,:)-Mt); end A=A+tA; Xt=X(tY~=i,:); mt=size(Xt,1); tA=zeros(n,n); tA=tA+(m-mt)*(Mt'*Mt); for j=1:mt tA=tA+(m-mt)/mt*(g2*(Xt(j,:)'*Xt(j,:))-g1*(Mt'*Xt(j,:)+Xt(j,:)'*Mt)); end B=B+tA; end %A=A+1e-5*eye(n); % regularization if needed [V,D]=eig(B,A); D=diag(D); [val,index]=sort(abs(D),'descend'); W=V(:,index); rX=X*W; end