LqLSSVM

Yuan-Hai Shao, Chun-Na Li,Zhen Wang, Ming-Zeng Liu, Nai-Yang Deng "Feature selection via sparse $L_q$-norm least squares support vector machines for small size samples" Submitted 2015.

function [Predict_Y,w,b,t]=QLSSVM(TestX,X,Y,FunPara) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % QLSSVM: q-norm LSSVM % [Predict_Y,w,b]=QLSSVM(TestX,DataTrain,FunPara); % Input: % TestX - Test Data matrix. Each row vector of fea is a data point. % % DataTrain - Struct value in Matlab(Training data). % DataTrain.X: Training input of Data matrix. % DataTrain.Y: Training output of Data vector, the value should be +1 and -1. % % FunPara - Struct value in Matlab. The fields in options that can be set: % FunPara.epsilon: small value the parameter in the QLSSVM. % FunPara.q: (0,1) the parameter in the QLSSVM. % FunPara.rho: [0,inf) the parameter in the QLSSVM. % FunPara.gamma: [0,inf) the parameter in the QLSSVM. % % Output: % Predict_Y - Predict value of the TestX. % w - weight vector. % b - bias. % % Examples: % load('example.mat'); % load('hepatitis.mat'); % DataTrain.X=X; % DataTrain.Y=Y; % TestX=X; % FunPara.epsilon=eps; % FunPara.q=0.5; % FunPara.rho=1; % FunPara.gamma=1; % [Predict_Y,w,b]=QLSSVM(TestX,DataTrain,FunPara); % % Reference: % Yuan-Hai Shao, Chun-Na Li, Zhen Wang, Ming-Zeng Liu, and Nai-Yang Deng, "Sparse q-norm least % squares support vector machines for feature selection" Submitted 2015 % % Version 1.0 --Jan/2015 % Written by Yuan-Hai Shao (shaoyuanhai21@163.com) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Initialization %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% [m,n]=size(X); %epsilon1 is an important parameter![0.001-0.00001] FunPara.epsilon=10e-7; u=ones(n+1,1); itt=1000; t=0; % first u1 u1=rand(n+1,1); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % training %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % tic aa=FunPara.q*FunPara.rho; % Yi must be +1 and -1 [e,ee]=size(Y(:,1)); e=ones(e,1); I=diag(ones(n,1)); H=[((Y'*X)'*(Y'*X)+1/FunPara.gamma*I),(Y'*X)'*(e'*Y); ((e'*Y)*X'*Y)',e'*Y*e'*Y]; clear I; d=[X e]'*Y; b=H'*d; % clear e d X Y H=H'*H; % H=(H+H')/2; % u1=H\d; while(t<=itt) && abs(norm(u1)-norm(u))>=eps cc=FunPara.epsilon+u1.^2; bb=cc.^(1-FunPara.q/2); A=diag(aa./bb); A=sparse(A); H=A+H; H=(H+H')/2; u=u1; % H=sparse(H); u1=H\b; t=t+1; % if sum(y)<(n+1)/2 % Theorem 3. % break % end end % clear H A b bb cc % toc %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % output and predict %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% w=u1(1:n); for i=1:n if abs(w(i)) < sqrt(FunPara.epsilon) w(i)=0; end end b=u1(n+1); Predict_Y=sign(TestX*w+ones(size(TestX,1),1)*b);

L12DLDA

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Main Function

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