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k_projectron2_train.m
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k_projectron2_train.m
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function model = k_projectron2_train(X,Y,model)
% K_PROJECTRON_TRAIN Kernel Projectron++ algorithm
%
% MODEL = K_PROJECTRON_TRAIN(X,Y,MODEL) trains an classifier according
% to the Projectron++ algorithm, using kernels.
%
% Additional parameters:
% - model.eta is the sparseness parameter, used to trade-off the
% performance for sparseness of the classifier.
% Default value is 0.1.
%
% References:
% - Orabona, F., Keshet, J., & Caputo, B. (2009).
% Bounded Kernel-Based Online Learning.
% Journal of Machine Learning Research 10(Nov), (pp. 2643–2666).
% This file is part of the DOGMA library for MATLAB.
% Copyright (C) 2009-2011, Francesco Orabona
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
%
% Contact the author: francesco [at] orabona.com
n = length(Y); % number of training samples
if isfield(model,'iter')==0
model.iter=0;
model.beta=[];
model.beta2=[];
model.errTot=0;
model.numSV=zeros(numel(Y),1);
model.aer=zeros(numel(Y),1);
model.pred=zeros(numel(Y),1);
model.Kinv=0;
end
if isfield(model,'eta')==0
model.eta=.1;
end
n_proj1=0;
n_proj2=0;
n_skip=0;
for i=1:n
model.iter=model.iter+1;
if numel(model.S)>0
K_f=feval(model.ker,model.SV,X(:,i),model.kerparam);
val_f=model.beta*K_f;
else
val_f=0;
K_f=0;
end
model.errTot=model.errTot+(sign(val_f)~=Y(i));
model.aer(model.iter)=model.errTot/model.iter;
model.pred(model.iter)=val_f;
if Y(i)*val_f<1 && Y(i)*val_f>0 % Margin Error
loss=(1-Y(i)*val_f);
Kii=feval(model.ker,X(:,i),X(:,i),model.kerparam);
coeff=K_f'*model.Kinv;
% 'max' to prevent numerical instabilities that could make delta a
% negative quantity.
delta=max(Kii-coeff*K_f,0);
norm_xt=max(Kii-delta,0);
if loss-delta/(model.eta)>0
alpha=min(min(loss/norm_xt,1),2*(loss-delta/(model.eta))/norm_xt);
model.beta=model.beta+alpha*Y(i)*coeff;
n_proj2=n_proj2+1;
else
n_skip=n_skip+1;
end
elseif Y(i)*val_f<=0 % Mistake
Kii=feval(model.ker,X(:,i),X(:,i),model.kerparam);
coeff=K_f'*model.Kinv;
% 'max' to prevent numerical instabilities that could make delta a
% negative quantity.
delta=max(Kii-coeff*K_f,0);
if delta<=model.eta
model.beta=model.beta+Y(i)*coeff;
n_proj1=n_proj1+1;
else
model.beta(end+1)=Y(i);
model.S(end+1)=model.iter;
model.SV(:,end+1)=X(:,i);
model.beta2(end+1)=0;
if numel(model.S)>1
tmp=[model.Kinv, zeros(numel(model.S)-1,1);zeros(1,numel(model.S))];
tmp=tmp+[coeff'; -1]*[coeff'; -1]'/delta;
else
tmp=feval(model.ker,model.SV,model.SV,model.kerparam)^-1;
end
model.Kinv=tmp;
end
end
model.beta2=model.beta2+model.beta;
model.numSV(model.iter)=numel(model.S);
if mod(i,model.step)==0
fprintf('#%.0f SV:%5.2f(%d)\tproj:%5.2f\tAER:%5.2f\n', ...
ceil(i/1000),numel(model.S)/i*100,numel(model.S),n_proj1/i*100,model.aer(model.iter)*100);
end
end