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**LpNPSVM**

A Matlab code for robust nonparallel proximal support vector machine with Lp-norm regularization.
(You could Right-Click [Code] , and Save, then you can download the whole matlab code.)

**Reference**

Xiao-Quan Sun, Yi-Jian Chen, Yuan-Hai Shao, Chun-Na Li*, Chang-Hui Wang. Robust nonparallel proximal support vector machine with Lp-norm regularization.

**Main Function**

**function [w1, w2, b1, b2, iter] = LpNPSVM(Atrain,Btrain,delta,p,w0,itmax,epsmax) **
**
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % % % LpNPSVM:
% Robust nonparallel proximal support vector machine with Lp-norm regularization
% [w1, b1, w2, b2] = LpNPSVM(Atrain,Btrain,FunPara,w0,itmax,epsmax)
% Input:
% Atrain: Positive class data matrix. Each row vector of Atrain is a data point.
% Btrain: Positive class data matrix. Each row vector of Btrain is a data point.
% delta: regularization term parameter.
% FunPara: parameters
% FunPara.delta: regularization parameter
% FunPara.p: p in Lp-norm regularization term
% w0: Initial hyperplane direction and bias
% itmax: Maximun iteration number
% epsmax: Tolerance
%
% % % % Eample:
% Atrain = rand(30,2);
% Btrain = rand(30,2) + 1;
% w0 = ones(1,size(Atrain,2) + 1); % Initialization
% FunPara.p = 1.5;
% FunPara.delta = 0.05;
% [w1, b1, w2, b2] = LpNPSVM(Atrain,Btrain,FunPara);
% Reference:
% Robust nonparallel proximal support vector machine with Lp-norm regularization. % IEEE Access, 2018, 6: 20334-20347.
% Xiao-Quan Sun, Yi-Jian Chen, Yuan-Hai Shao, Chun-Na Li*, Chang-Hui Wang
% Version 2.0 --June/2018
% Written by Chun-Na Li (na1013na@163.com)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
****
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Initailization
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
****
if nargin == 2
FunPara.delta = 0.05; FunPara.p = 1.5; w0 = ones(size(Atrain,2) + 1,1); itmax = 100; epsmax = 10^(-5);
elseif nargin == 3
w0 = ones(size(Atrain,2) + 1,1); itmax = 100; epsmax = 10^(-5);
elseif nargin == 4
itmax = 100; epsmax = 10^(-5);
elseif nargin == 5
epsmax = 10^(-5);
end
delta = FunPara.delta;
p = FunPara.p;
[nSmpA, nFea] = size(Atrain);
[nSmpB, ~] = size(Btrain);
wp0 = w0;
wn0 = w0;
epsWX = 10^-4;
epsW = 10^-4;
Atrainbar = [Atrain,ones(size(Atrain,1),1)]';
Btrainbar = [Btrain,ones(size(Btrain,1),1)]';
while 1
%%%%%%%%%%%%%%%%%%
% % % For A
%%%%%%%%%%%%%%%%%%
Ht_A = zeros(nFea+1, nFea+1);
ht_A = zeros(nFea+1,1);
for i = 1:nSmpA
Atrainbari = Atrainbar(:,i);
Ht_A = Ht_A + (Atrainbari*Atrainbari')/abs(wp0'*Atrainbari + epsWX);
end
for i = 1:nSmpB
ht_A = ht_A + sign(wp0'*Btrainbar(:,i))*Btrainbar(:,i);
end
q_A = (abs(wp0) + epsW).^(p - 2);
Ht_Ar = delta*diag(q_A);
Ht_A = Ht_A + Ht_Ar;
wp = (Ht_A\ht_A)/(ht_A'*inv(Ht_A)*ht_A);
wp0 = wp;
%%%%%%%%%%%%%%%%%%
% % % For B
%%%%%%%%%%%%%%%%%%
Ht_B = zeros(nFea+1, nFea+1);
ht_B = zeros(nFea+1,1);
for i = 1:nSmpB
Btrainbari = Btrainbar(:,i);
Ht_B = Ht_B + (Btrainbari*Btrainbari')/abs(wp0'*Btrainbari + epsWX);
end
for i = 1:nSmpA
ht_B = ht_B + sign(wn0'*Atrainbar(:,i))*Atrainbar(:,i);
end
q_B = (abs(wn0) + epsW).^(p - 2);
Ht_Br = delta*diag(q_B);
Ht_B = Ht_B + Ht_Br;
wn = (Ht_B\ht_B)/(ht_B'*inv(Ht_B)*ht_B);
wn0 = wn;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if max(abs(wp-wp0))itmax
break;
end
end
w1 = wp(1:length(wp)-1);
b1 = wp(length(wp));
w2 = wn(1:length(wn)-1);
b2 = wn(length(wn));
**

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- Last updated: 2, June, 2018