L1NPSVM

Chun-Na Li, Yuan-Hai Shao, Nai-Yang Deng. Robust L1-norm nonparallel proximal support vector machine[J]. Optimization. 2014.

function [ClassAC,fw] = L1NPSVM(Data,d) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % L1NPSVM: L1-norm nonparallel proximal svm % % Predict_Y=L1NPSVM(TestX,DataTrain) % % w is a column vector % % Reference: % % Version 1.0 --16.Dec/2013 % Written by Wei-Jie Chen and Chun-Na Li, wjcper2008@126.com and na1013na@163.com. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Initialization %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %tic; [~,nFea] = size(Data.TrainX); gamma = 0.0005; % Learning rate classLabel = unique(Data.TrainY); nClass = length(classLabel); ClassAC = zeros(d,1); fw = zeros(nFea+1,d,nClass); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Greedy Search Algorithm find multiple features for each class %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for c = 1:nClass A = Data.TrainX((Data.TrainY==classLabel(c)),:); A = [A, ones(length(A(:,1)),1)]; B = Data.TrainX((Data.TrainY~=classLabel(c)),:); B = [B, ones(length(B(:,1)),1)]; % Greedy Search Algorithm Come On!!! for k=1:d obj = 0; w = rand(nFea+1,1); w = w/norm(w); while 1 %Polarity check S = sign(A*w);R = sign(B*w); %Updata wn TempL = sum(diag(S)*A); TempR = sum(diag(R)*B); Ldenomi = TempL*w; Rdenomi = TempR*w; %Check two denominators in equ (9) whether to 0 if (Ldenomi ==0) || (Rdenomi ==0) w = w + (rand(nFea, 1)-0.5)*0.002; fprintf('Convergence break,De:%d\n',k); continue; end G = TempR/Rdenomi -TempL/Ldenomi; wn = w + gamma*G'; %Convergence check objn = sum(abs(A*wn))/sum(abs(B*wn)); if abs(objn - obj) < 0.0001 % fprintf('Convergence,De:%d\n',k); break; end obj = objn; w = wn; end fw(:,k,c) = wn/norm(wn); A = A - (A*wn)*wn'; B = B - (B*wn)*wn'; end clear A B end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % output and predict %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% nTest = length(Data.TestX(:,1)); TestX =[Data.TestX, ones(nTest,1)]; DemTeX = zeros(nTest,c); for k=1:d for c=1:nClass DemTeX(:,c) = TestX*fw(:,1:k,c); %redundency X end [~,PTestY] = min(abs(DemTeX),[],2); %Classification ClassAC(k) = sum(PTestY == Data.TestY)/length(PTestY); end end

TWSVC

Reference

Main Function

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