RSLDA

A Matlab code of Robust and sparse linear discriminant analysis via alternating direction method of multipliers

Reference

Chun-Na Li, Yuan-Hai Shao*, Wo-Tao Yin, and Ming-Zeng Liu. Robust and sparse linear discriminant analysis via alternating direction method of multipliers[J]. Submitted. [Slides]

Exam

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function [W] = RSLDA(Data, Prjdim, RSLDAPara) % % RLDA and RSLDA: Robust and sparse linear discriminant analysis via % alternating direction method of multiplier % Input: % Data: Data.trainX - the training samples; % Data.trainY - the labels corresponding to training samples; % Prjdim: - the dimension to be projected; % RSLDAPara.method - 0 or 1, 0 to perform RLDA, and 1 to perform RSLDA % RSLADPara: the parameters for RLDA and RSLDA. % RSLDAPara.rho - the augment lagrangian parameter; % RSLDAPara.lambda - the lambda for RLDA and RSLDA. % RSLDAPara.sigm - the sigma for RLDA and RSLDA. % RSLDAPara.tol - the epsilon for RLDA and RSLDA. %Ouput: % W: -the project vectors: dim x Prjdim; % dim: the dimension of samples; % Prjdim: the number of projection vector; % Example: % Data.trainX = rand(50,10); % Data.trainY = [ones(25,1);-ones(25,1)] % Prjdim = 5; % RSLDAPara.method = 1; % RSLDAPara.rho = 5; % RSLDAPara.lambda = 0.5; % RSLDAPara.sigm = 0.05;; % RSLDAPara.tol = 1e-3; % Predict_Y = RSLDA(Data, Prjdim, RSLDAPara); % % Reference: % Li C N, Shao Y H, Yin W T, Liu M Z. Robust and sparse linear discriminant % analysis via alternating direction method of multipliers. % % Version 1.0 -- Oct/2017 % Written by Ming-Zeng Liu and Chun-Na Li (mzliu@dlut.edu.cn and na1013na@163.com) %% function begin .... rho = RSLDAPara.rho; lambda = RSLDAPara.lambda; sigm = RSLDAPara.sigm; tol = RSLDAPara.tol; fea = Data.trainX; gnd = Data.trainY; [nsams, dim] = size(fea); I = eye(dim); [nsamsc,labels] = hist(gnd, unique(gnd)); nc = numel(labels); % Proj vector matrix; W = zeros(dim,Prjdim); for k = 1:Prjdim clsmean = zeros(nc, dim); % mean for each class Sw = zeros(dim,dim); % Sw: Scatter matrix within class for i = 1:nc %% calculate the mean of each class cls_idx = (gnd == labels(i)); clsmean(i,:) = mean(fea(cls_idx,:),1); Sw = Sw + (fea(cls_idx,:)-repmat(clsmean(i,:),nsamsc(i),1))'*... (fea(cls_idx,:)-repmat(clsmean(i,:),nsamsc(i),1)); end Sw = Sw/nsams; X0 = (clsmean - repmat(mean(fea,1),nc,1))' * diag(nsamsc); % rand initial w = rand(dim,1); u2 = rand(dim,1); y = rand(nc,1); u1 = rand(nc,1); % convergence conditions % eps_pri_one, eps_pri_two eps_dual_one, eps_dual_two eps_pri_one = 1.0; eps_pri_two = 1.0; eps_dual_one = 1.0; eps_dual_two = 1.0; % iteration count iter_while = 1; Ginv = (X0*X0' + I + 2*lambda/rho * Sw)\I; while ( (eps_pri_one > tol) || ... (eps_pri_two > tol) || ... (eps_dual_one > tol) || ... (eps_dual_two > tol) ) %% solve z z = Ginv * (X0 * (y - u1) + (w - u2)); % Ginv * g %% solve y y0 = y; Xz = X0'*z; y = Xz + u1; y(y>=0) = y(y>=0) + 1/rho; y(y<0) = y(y<0) - 1/rho; %% solve w w0 = w; w = z - u2; % The solution of w to RLDA % For RSLDA, the following codes are also needed if RSLDAPara.method == 1 ka = sigm/rho; w(w > ka) = w(w > ka) - ka; w(w < -ka) = w(w < -ka) + ka; w( w<=ka & w>=-ka) = 0; end %% solve u1 and u2 u1 = u1 + Xz - y; u2 = u2 + w - z; % eps_pri_one_old = eps_pri_one; eps_pri_two_old = eps_pri_two; eps_dual_one_old = eps_dual_one; eps_dual_two_old = eps_dual_two; eps_pri_one = norm(Xz - y); eps_pri_two = norm(w - z); eps_dual_one = norm( X0*(y - y0)); eps_dual_two = norm(w - w0); if iter_while > 1000 break; end if ( (abs(eps_pri_one - eps_pri_one_old ) < 1E-3) && ... (abs(eps_pri_two - eps_pri_two_old ) < 1E-3) && ... (abs(eps_dual_one - eps_dual_one_old ) < 1E-3 )&& ... (abs(eps_dual_two - eps_dual_two_old ) < 1E-3) ) break; end iter_while = iter_while + 1; end % end while W(:,k) = w; fea = fea - (fea * w) * w'; end fprintf('\n'); end

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