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**MLSPTSVM**

A Matlab code for Multi-class least squares recursive projection twin support vector machine . [Code]

**Reference**

Yuan-Hai Shao, Nai-Yang Deng*, Zhi-Min Yang. Least squares recursive projection twin support vector machine for classification[J]. **Pattern Recognition**, 2012, 45(6): 2299-2307.

Chun-Na Li, Yun-Feng Huang, He-Ji Wu, Yuan-Hai Shao, Zhi-Min Yang. Multiple recursive projection twin support vector machine for multi-class classification. **International Journal of Machine Learning and Cybernetics**, 2014,DOI: 10.1007/s13042-014-0289-2.

**Main Function**

**[Predict_Y] = K_CLASSLSPTSVM(TestX,DataTrain,FunPara)**
**
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% MLSPTSVM: Multi-class least squares recursive projection twin support vector machine
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%
%%%%%%%%% Inputs: %%%%%%%%%%
% TestX: Denote the input features of testing patterns.
% DataTrain: Include the input features (DataTrain.X) and corresponding
class labels (DataTrain.Y) of training patterns, and the number
of classes (DataTrain.Type).
% FunPara: Gather all the parameters we used, including penalty
parameters c and v ( FunPara.c and FunPara.v), kernel type
(lin or rbf)£¬kernel width pars (only for rbf kernel) and
desired number of projention axes(FunPara.loop).
%%%%%%%%% Outputs: %%%%%%%%%
% Predict_Y: The corresponding predict labels of TestX.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%% Example: %%%%%%%%%
% DataTrain.X = rand(100,10);
% DataTrain.Y = [ones(20,1);2*ones(20,1);3*ones(20,1);4*ones(20,1);5*ones
(20,1)];
% DataTrain.Type = 5;
% FunPara.c = 10; FunPara.v = 9;
% FunPara.kerfPara.type = 'rbf';FunPara.kerfPara.pars = 10;
% TestX = rand(60,10);
% FunPara.loop = 2;
% [Predict_Y] = K_CLASSLSPTSVM(TestX,DataTrain,FunPara)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%% Algorithm Starting %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%% Training %%%%%%%%%%%%%%%%%%%%
****
kerfPara = FunPara.kerfPara;
m = size(DataTrain.X,1);
n = size(TestX,1);
TestBack = TestX;
C = DataTrain.X;
Dis = zeros(n,DataTrain.Type);
****
% Distance matrix between projection of test patterns and projected centers.
****
Predict_Y = zeros(n,1);
for i = 1:DataTrain.Type
****
% Determine the projection axes for each class.
****
W1=[];
loop = FunPara.loop;
SubclassIndex = find(DataTrain.Y==i);
trainXA = DataTrain.X(SubclassIndex,:);
****
% Training patterns of the i-th class.
****
trainXB = DataTrain.X(setdiff(1:m,SubclassIndex),:);
****
% Training patterns of all the classes except for the i-th class.
****
if ~strcmp(kerfPara.type,'lin')
****
% Nonliner kernel: Gaussian, Polynomial and so on.
****
if m >= 1000
****
% Whether to use rectangular kernel technique.
****
ReduceIndex = randperm(m,int16(0.05*m));
****
% Select 5% of the training patterns.
****
C = DataTrain.X(ReduceIndex,:);
end
trainXA = kernelfun(trainXA,kerfPara,C);
****
% Training patterns of the i-th class in the kernel space.
****
trainXB = kernelfun(trainXB,kerfPara,C);
TestX = kernelfun(TestBack,kerfPara,C);
end
w1 = zeros(size(trainXA,2),1);
****
% Initialize the projection axis of the i-th class.
****
centerA = mean(trainXA);
while loop>0
****
% Seeking multiple projection axes for each class.
****
trainXA = trainXA - trainXA*w1*w1';
****
% Update samples by recursive.
****
trainXB = trainXB - trainXB*w1*w1';
****
% Update samples by recursive.
****
m1 = size(trainXA,1); m2 = size(trainXB,1);
e1 = ones(m1,1); e2 = ones(m2,1);
I1 = eye(size(trainXB,2));
meanA = 1/m1*e1'*trainXA;
H = trainXA - e1*meanA;
G = trainXB - e2*meanA;
Y = H'*H /FunPara.c + FunPara.v/FunPara.c*I1;
****
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Determine the projection axes for the i-th class %%%%%%%%%%%%%%%%%
****
if ~strcmp(kerfPara.type,'lin') && m < 1000
****
% Whether to employ the SMW technique for nonlinear case.
****
I2 = eye(size(trainXA,1));
I3 = eye(size(trainXB,1));
HH = I2 + H*H'/FunPara.v;
YY = FunPara.c/FunPara.v*(I1 - H'*(HH\H)/FunPara.v);
****
% Require one matrix inverse of order m1*m1.
****
GG = I3 + G*YY*G';
w1 = (YY - YY*G'*(GG\G)*YY)*G'*e2;
****
% Require two matrix inverses of order m1*m1 and m2*m2 (m=m1+m2).
****
else
w1 = (Y+G'*G)\G'*e2;
****
% Require one matrix inverse of order m*m.
****
end
w1 = w1/norm(w1);
W1 = [W1 w1];
****
% All the desired projection axes of the i-th class.
****
loop = loop-1;
end
clear trainXA trianXB H G Y HH YY GG;
for t = 1:n
Dis(t,i) = norm(TestX(t,:)*W1 - centerA*W1);
end
end
****
%%%%%%%%%%% output and predict %%%%%%%%%
****
for s = 1:n
Predict_Y(s,1) = find(Dis(s,:)==min(Dis(s,:)));
end
**

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- Last updated: Dec 27, 2014