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k_projectron2_multi_train.m
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k_projectron2_multi_train.m
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function model = k_projectron2_multi_train(X,Y,model)
% K_PROJECTRON2_MULTI_TRAIN Kernel Projectron++ multiclass algorithm
%
% MODEL = K_PROJECTRON2_MULTI_TRAIN(X,Y,MODEL) trains an classifier
% according to the Projectron++ multiclass algorithm, using kernels.
%
% Additional parameters:
% - model.eta is the sparseness parameter, used to trade-off the
% performance for sparseness of the classifier. Note that model.eta is
% the maximum error on EACH single projection; each projected update
% has 2 projections.
% 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,'n_cla')==0
model.n_cla=max(Y);
end
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(model.n_cla,numel(Y));
for i=1:model.n_cla
model.Kinv{i}=[];
model.Y_cla{i}=[];
end
end
if isfield(model,'eta')==0
model.eta=.1;
end
n_skip=0;
n_proj1=0;
n_proj2=0;
n_pred=0;
idx_true=[];
idx_wrong=[];
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=full(model.beta*K_f);
else
val_f=zeros(1,model.n_cla);
K_f=[];
end
Yi=Y(i);
tmp=val_f; tmp(Yi)=-inf;
[mx_val,idx_mx_val]=max(tmp);
model.errTot=model.errTot+(val_f(Yi)<=mx_val);
model.aer(model.iter)=model.errTot/model.iter;
model.pred(:,model.iter)=val_f;
if val_f(Yi) < mx_val+1 %Margin error or mistake
Kii=full(feval(model.ker,X(:,i),X(:,i),model.kerparam));
delta_true=Kii;
delta_wrong=Kii;
if numel(model.S)>0
idx_true=model.Y_cla{Yi};
idx_wrong=model.Y_cla{idx_mx_val};
if numel(idx_true)>0
coeff_true=K_f(idx_true)'*model.Kinv{Yi};
% 'max' to prevent numerical instabilities that could make
% delta a negative quantity.
delta_true=max(Kii-coeff_true*K_f(idx_true),0);
end
if numel(idx_wrong)>0
coeff_wrong=K_f(idx_wrong)'*model.Kinv{idx_mx_val};
% 'max' to prevent numerical instabilities that could make
% delta a negative quantity.
delta_wrong=max(Kii-coeff_wrong*K_f(idx_wrong),0);
end
end
if val_f(Yi)>mx_val % Margin error
loss=1-val_f(Yi)+mx_val;
delta=delta_wrong+delta_true;
% 2*model.eta because eta is the tollerance on each single
% projection.
if loss-delta/(2*model.eta)>0
tau_m=min(min(loss/(2*Kii-delta),1),2*(loss-delta/(2*model.eta))/(2*Kii-delta));
if numel(idx_true)>0
model.beta(Yi,idx_true)=model.beta(Yi,idx_true)+tau_m*coeff_true;
end
if numel(idx_wrong)>0
model.beta(idx_mx_val,idx_wrong)=model.beta(idx_mx_val,idx_wrong)-tau_m*coeff_wrong;
end
n_proj2=n_proj2+1;
else
n_skip=n_skip+1;
end
else %Mistake
vec=spalloc(1,model.n_cla,2);
if (delta_true <= model.eta && delta_wrong <= model.eta) || delta_true < eps
if numel(idx_true)>0
model.beta(Yi,idx_true)=model.beta(Yi,idx_true)+coeff_true; % project true
end
else
vec(Yi)=1; % normal update for true
if numel(model.Kinv{Yi})~=0
tmp=[model.Kinv{Yi}, zeros(size(model.Kinv{Yi},1),1);zeros(1,size(model.Kinv{Yi},1)+1)];
tmp=tmp+[coeff_true'; -1]*[coeff_true'; -1]'/delta_true;
else
tmp=full(Kii^-1);
end
model.Kinv{Yi}=tmp;
model.Y_cla{Yi}(end+1)=size(model.SV,2)+1;
end
if (delta_true <= model.eta && delta_wrong <= model.eta) || delta_wrong < eps
if numel(idx_wrong)>0
model.beta(idx_mx_val,idx_wrong)=model.beta(idx_mx_val,idx_wrong)-coeff_wrong; % project wrong
end
else
vec(idx_mx_val)=-1; % normal update for wrong
if numel(model.Kinv{idx_mx_val})~=0
tmp=[model.Kinv{idx_mx_val}, zeros(size(model.Kinv{idx_mx_val},1),1);zeros(1,size(model.Kinv{idx_mx_val},1)+1)];
tmp=tmp+[coeff_wrong'; -1]*[coeff_wrong'; -1]'/delta_wrong;
else
tmp=full(Kii^-1);
end
model.Kinv{idx_mx_val}=tmp;
model.Y_cla{idx_mx_val}(end+1)=size(model.SV,2)+1;
end
if delta_true > model.eta || delta_wrong > model.eta
model.beta(:,end+1)=vec;
model.S(end+1)=model.iter;
model.SV(:,end+1)=X(:,i);
model.beta2(:,end+1)=0;
else
n_proj1=n_proj1+1;
end
end
else
n_pred=n_pred+1;
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) pred:%5.2f skip:%5.2f proj1:%5.2f proj2:%5.2f AER:%5.2f\n', ...
ceil(i/1000),numel(model.S)/i*100,numel(model.S),n_pred/i*100,n_skip/i*100,n_proj1/i*100,n_proj2/i*100,model.aer(model.iter)*100);
if isfield(model,'eachRound')~=0
feval(model.eachRound,model);
end
end
end