[Home]


L1BLDA

A Matlab code for Robust Bhattacharyya bound LDA through an adaptive non-greedy algorithm. [Code]


Reference

Chun-Na Li, Yuan-Hai Shao, Zhen Wang, Nai-Yang Deng£¨Zhi-Min Yang. "Robust Bhattacharyya bound linear discriminant analysis through an adaptive non-greedy algorithm". Submitted, 2018.


Main Function

function [W_all] = L1BLDA(Data,FunPara) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % % Input: % Data.X: Data matrix. Each column vector of Data is a data point. % Data.Y: Data label vector. % FunPara.rho: ADMM penalty rho. % % % % % Eample: % Data.X = rand(2,20); % Data.Y = [ones(10,1);-ones(10,1)]; % FunPara.rho = 1; % [W_all] = L1BLDA(Data,FunPara) % % % % % Reference: % "Robust Bhattacharyya bound linear discriminant analysis through adaptive non-greedy algorithms". % Chun-Na Li, Yuan-Hai Shao, Zhen Wang, Nai-Yang Deng % Version 1.0 -- July/2018 % Written by Chun-Na Li (na1013na@163.com) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Maxstep = 20; rho = FunPara.rho; eps1 = 10^(-3); eps2 = 10^(-3); [nFea,nSmp] = size(Data.trainX); desireDim = nFea; W_all = cell(desireDim,1); classLabel = unique(Data.trainY); nClass = length(classLabel); C_mean = zeros(nFea,nClass); nSmpClass = zeros(1,nClass); subX = Data.trainX; Sw = zeros(nFea,nFea); Sb = zeros(nFea,nFea); Omega = 0; % Calculate Sw for i=1:nClass Index(i,:) = (Data.trainY==classLabel(i)); C_mean(:,i) = mean(subX(:,Index(i,:)),2); nSmpClass(i) = size((subX(:,Index(i,:))),2); TempM = subX(:,Index(i,:)) - repmat(C_mean(:,i),1,nSmpClass(i)); Sw = Sw + TempM*TempM'; end % Calculate Sb and Omega for i = 1:nClass for j = 1:nClass if i eps1 || P_con2 > eps1 || P_con3 > eps1 || D_con1 > eps1 || D_con2 > eps1 || D_con3 > eps1 ) % ADMM, W B0 = B; for i = 1:nClass for j = 1:nClass if i=0) = B(B>=0) + 1/rho_new; B(B<0) = B(B<0) - 1/rho_new; % ADMM, Z Z0 = Z; for i=1:nClass Temp = subX(:,Index(i,:)); for j=1:nSmpClass(i) Z(i,j,:) = W'*(Temp(:,j)-C_mean(:,i))+beta(i,j); D_con20(i,j) = norm(rho_new*(Temp(:,j)-C_mean(:,i))*(Z(i,j)-Z0(i,j))'); end end ka = Omega/rho_new; Z(Z > ka) = Z(Z > ka) - ka; Z(Z < -ka) = Z(Z < -ka) + ka; Z(Z<=ka & Z>=-ka) = 0; % ADMM, D D0 = D; D = W - Gamma; Po_con1 = P_con1; Po_con2 = P_con2; Po_con3 = P_con3; Do_con1 = D_con1; Do_con2 = D_con2; Do_con3 = D_con3; for i=1:nClass xi = subX(:,Index(i,:)); for j=1:nSmpClass(i) tempijbeta = W'*(xi(:,j)-C_mean(:,i))-Z(i,j); beta(i,j,:) = beta(i,j)+tempijbeta; P_con20(i,j) = norm(tempijbeta); end end Gamma = Gamma + (D-W); P_con1 = max(max(P_con10)); P_con2 = max(max(P_con20)); P_con3 = norm(D-W); D_con1 = max(max(D_con10)); D_con2 = max(max(D_con20)); D_con3 = norm(rho_new*(D-D0)); P_con = max(P_con1,max(P_con2,P_con3)); D_con = max(D_con1,max(D_con2,D_con3)); mu=10;t_incr=2;t_decr=2; if P_con>mu*D_con rho_new=t_incr*rho_new; elseif D_con>mu*P_con rho_new=rho_new/t_decr; else rho_new=rho_new; end if abs(Po_con1 - P_con1) < eps2 && abs(Po_con2 - P_con2) < eps2 && abs(Po_con3 - P_con3) < eps2 < eps2 && abs(Do_con1 - D_con1) < eps2 && abs(Do_con2 - D_con2) < eps2 && abs(Do_con3 - D_con3) < eps2 break; end if step>Maxstep break end step = step +1; TP_con1(step) = P_con1; TP_con2(step) = P_con2; TP_con3(step) = P_con3; TD_con1(step) = D_con1; TD_con2(step) = D_con2; TD_con3(step) = D_con3; end W_all{d} = W; clear W B alpha Z beta D Gamma else % when d = n for i = 1:nClass for j = 1:nClass if i eps1 || P_con2 > eps1 || P_con3 > eps1 || D_con1 > eps1 || D_con2 > eps1 || D_con3 > eps1 ) % ADMM, W B0 = B; for i = 1:nClass for j = 1:nClass if i=0) = B(B>=0) + 1/rho_new; B(B<0) = B(B<0) - 1/rho_new; % ADMM, Z Z0 = Z; for i=1:nClass Temp = subX(:,Index(i,:)); for j=1:nSmpClass(i) Z(i,j,:) = W'*(Temp(:,j)-C_mean(:,i))+beta(i,j); D_con20(i,j) = norm(rho_new*(Temp(:,j)-C_mean(:,i))*(Z(i,j)-Z0(i,j))); end end ka = Omega/rho_new; Z(Z > ka) = Z(Z > ka) - ka; Z(Z < -ka) = Z(Z < -ka) + ka; Z(Z<=ka & Z>=-ka) = 0; % ADMM, D D0 = D; D = W - Gamma; Po_con1 = P_con1; Po_con2 = P_con2; Po_con3 = P_con3; Do_con1 = D_con1; Do_con2 = D_con2; Do_con3 = D_con3; for i=1:nClass xi = subX(:,Index(i,:)); for j=1:nSmpClass(i) tempijbeta = W'*(xi(:,j)-C_mean(:,i))-Z(i,j); beta(i,j,:) = beta(i,j)+tempijbeta; P_con20(i,j) = norm(tempijbeta); end end Gamma = Gamma + (D-W); P_con1 = max(max(P_con10)); P_con2 = max(max(P_con20)); P_con3 = norm(D-W); D_con1 = max(max(D_con10)); D_con2 = max(max(D_con20)); D_con3 = norm(rho_new*(D-D0)); P_con = max(P_con1,max(P_con2,P_con3)); D_con = max(D_con1,max(D_con2,D_con3)); mu=10;t_incr=2;t_decr=2; if P_con>mu*D_con rho_new=t_incr*rho_new; elseif D_con>mu*P_con rho_new=rho_new/t_decr; else rho_new=rho_new; end if abs(Po_con1 - P_con1) < eps2 && abs(Po_con2 - P_con2) < eps2 && abs(Po_con3 - P_con3) < eps2 < eps2 && abs(Do_con1 - D_con1) < eps2 && abs(Do_con2 - D_con2) < eps2 && abs(Do_con3 - D_con3) < eps2 break; end if step>Maxstep break end step = step +1; TP_con1(step) = P_con1; TP_con2(step) = P_con2; TP_con3(step) = P_con3; TD_con1(step) = D_con1; TD_con2(step) = D_con2; TD_con3(step) = D_con3; end W_all{d} = W; end end function [W] = QPSM(G,A) itmax = 10; eps = 10^-4; it2 = 0; [m,k] = size(A); [~,D_G] = eig(G); D_G = diag(D_G); alpha = max(D_G) + 0.01; W = [eye(k);zeros(m-k,k)]; while it2 < itmax it2 = it2 + 1; W0 = W; M = 2*(alpha*eye(m) - G)*W - 2*A; [U,~,V] = svd(M,0); W = U*V'; if norm(W - W0) < eps break; end end
Contacts


Any question or advice please email to na1013na@163.com or shaoyuanhai21@163.com.