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k_forgetron_st_train.m
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k_forgetron_st_train.m
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function model = k_forgetron_st_train(X,Y,model)
% K_FORGETRON__ST_TRAIN Kernel Forgetron algorithm, 'self-tuned' variant
%
% MODEL = K_FORGETRON_TRAIN(X,Y,MODEL) trains an classifier according
% to the Forgetron algorithm, 'self-tuned' variant, using kernels.
%
% Additional parameters:
% - model.maxSV is the maximum number of Support Vectors. When the
% algorithm reaches that quantity it starts discarding random vectors,
% according to the Forgetron algorithm.
% Default value is 1/10 of the training samples.
%
% References:
% - Dekel, O., Shalev-Shwartz, S., & Singer, Y. (2007).
% The Forgetron: A kernel-based perceptron on a budget.
% SIAM Journal on Computing 37, (pp. 1342–1372).
% 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.errTot=0;
model.numSV=zeros(numel(Y),1);
model.aer=zeros(numel(Y),1);
model.pred=zeros(numel(Y),1);
model.out=[];
model.Q=0;
end
if isfield(model,'maxSV')==0
model.maxSV=numel(Y)/10;
end
for i=1:n
model.iter=model.iter+1;
if numel(model.S)>0
if isempty(model.ker)
K_f=X(model.S,i);
else
K_f=feval(model.ker,model.SV,X(:,i),model.kerparam);
end
val_f=model.beta*K_f;
else
val_f=0;
end
model.errTot=model.errTot+(sign(val_f)~=Y(i));
model.aer(model.iter)=model.errTot/model.iter;
if Y(i)*val_f<=0
model.beta(end+1)=Y(i);
model.S(end+1)=model.iter;
if ~isempty(model.ker)
model.SV(:,end+1)=X(:,i);
end
if numel(model.S) > model.maxSV
if isempty(model.ker)
K_f=X(model.S,model.S(1));
else
K_f=feval(model.ker,model.SV,model.SV(:,1),model.kerparam);
end
fp=model.beta*K_f;
a=model.beta(1)^2-2*model.beta(1)*fp;
b=2*abs(model.beta(1));
c=model.Q-15/32*model.errTot;
d=b^2-4*a*c;
if a>0 || (a<0 && d>0 && (-b-sqrt(abs(d)))/(2*a)>1)
phi=min(1,(-b+sqrt(d))/(2*a));
elseif a==0
phi=min(1,-c/b);
else
phi=1;
end
model.beta=model.beta*phi;
fpp=model.beta*K_f;
e=abs(model.beta(1));
model.Q=model.Q+e^2+2*e-2*e*sign(model.beta(1))*fpp;
model.beta(1)=[];
model.S(1)=[];
if ~isempty(model.ker)
model.SV(:,1)=[];
end
end
end
model.numSV(model.iter)=numel(model.S);
if mod(i,model.step)==0
fprintf('#%.0f SV:%5.2f(%d)\tAER:%5.2f\n', ...
ceil(i/1000),numel(model.S)/model.iter*100,numel(model.S),model.aer(model.iter)*100);
end
end