-
Notifications
You must be signed in to change notification settings - Fork 2
/
k_oisvm_train.m
executable file
·206 lines (172 loc) · 7.08 KB
/
k_oisvm_train.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
function model = k_oisvm_train(X,Y,model)
% K_OISVM_TRAIN Kernel Online Independent SVM algorithm
%
% MODEL = K_OISVM_TRAIN(X,Y,MODEL) trains an classifier according to the
% Online Independent SVM algorithm, using kernels.
%
% Additional parameters:
% - model.C is the weight of the error, used to reduce the amount of
% regularization.
% Default value is 1.
% - 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., Castellini, C., Caputo, B., Jie, L., & Sandini, G. (2010).
% Online Independent Support Vector Machines.
% Pattern Recognition 43(4), (pp. 1402-1412).
% 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.num_ker_eval=0;
model.X=[];
model.Y=[];
model.K=zeros(100,100);
model.x=0;
model.sv=[];
model.ss=0;
model.KbInv=[];
end
if isfield(model,'C')==0
model.C=1;
end
if isfield(model,'eta')==0
model.eta=.1;
end
C=model.C;
ker=model.ker;
kerparam=model.kerparam;
if ~isfield(model,'maxiter'), model.maxiter = 20; end
if ~isfield(model,'rows_mem'), model.rows_mem = 100; end
if ~isfield(model,'cols_mem'), model.cols_mem = 100; end
maxRow=size(model.K,1);
maxCol=size(model.K,2);
for curr=1:n
model.iter=model.iter+1;
dimS=length(model.S);
model.X=[model.X , X(:,curr)];
model.Y=[model.Y , Y(curr)];
ultimo=size(model.X,2);
last_col=[Y(curr); feval(ker,model.X,model.S,ultimo,kerparam) * Y(curr)];
model.num_ker_eval=model.num_ker_eval+numel(model.S);
model.K(1:dimS+1,ultimo)=last_col;
if ultimo==maxCol
tmp=zeros([size(model.K,1) size(model.K,2)+model.cols_mem]);
tmp(1:dimS+1,1:ultimo)=model.K(1:dimS+1,1:ultimo);
%tmp(:,1:curr)=K(:,1:curr); %is it faster copying even the zeros?
model.K=tmp;
maxCol=size(model.K,2);
end
if dimS>0
colonna2=model.K(2:dimS+1,ultimo)*Y(curr);
amin=model.KbInv*colonna2;
delta=feval(ker,X,curr,curr,kerparam)-colonna2'*amin;
model.num_ker_eval=model.num_ker_eval+1;
if (delta>model.eta)
model.KbInv=[model.KbInv, zeros(dimS,1);zeros(1,dimS+1)];
model.KbInv=model.KbInv+[amin; -1]*[amin; -1]'/delta;
model.S = [model.S ultimo];
riga=feval(ker,model.X,ultimo,1:ultimo,kerparam).*model.Y(1:ultimo);
model.num_ker_eval=model.num_ker_eval+ultimo;
model.K(dimS+2,1:ultimo)=riga;
% update Cholesky decomposition of the hessian
d = length(model.S);
h = [0; model.K(d+1,model.S)'.*model.Y(model.S)'] + C * model.K(1:d+1,model.sv) * model.K(d+1,model.sv)';
h2 = h(end,:);
h2 = h2 + 1e-10*h2*eye(size(h,2)); % Ridge is only for numerical reason
h3 = model.hess' \ h(1:d,:);
h4 = sqrt(h2-h3'*h3);
model.hess = [[model.hess h3]; [zeros(1,d) h4]];
model.ss=[model.ss;sum(riga(model.sv))];
if dimS+2==maxRow
tmp=zeros([size(model.K,1)+model.rows_mem size(model.K,2)]);
tmp(1:size(model.K,1),1:ultimo)=model.K(1:size(model.K,1),1:ultimo);
model.K=tmp;
maxRow=size(model.K,1);
end
end
else
model.S = ultimo;
riga=feval(ker,model.X,ultimo,1:ultimo,kerparam).*model.Y(1:ultimo)';
model.num_ker_eval=model.num_ker_eval+ultimo;
model.K(2,1:ultimo)=riga;
% update Cholesky decomposition of the hessian
model.hess=[1e-5,0;0,sqrt(model.K(2,1)*Y(1))];
model.ss=[model.ss;sum(riga(model.sv))];
model.KbInv=(model.K(2,1)*Y(1))^-1;
end
outNew = model.K(1:length(model.x),ultimo)'*model.x;
model.errTot=model.errTot+(sign(outNew)<=0);
model.aer(model.iter)=model.errTot/model.iter;
model.pred(model.iter)=outNew*Y(curr);
if outNew<1
K2 = model.K(1:size(model.hess,1),1:ultimo);
model.hess = cholupdate(model.hess,sqrt(C)*K2(:,ultimo),'+');
model.ss = model.ss+K2(:,ultimo);
iter = 0;
model.sv = [model.sv,ultimo];
sv_bool = zeros(1,ultimo);
sv_bool(model.sv) = 1;
while iter < model.maxiter
iter = iter + 1;
% Take a few Newton step (no line search). By writing out the
% equations, this simplifies to following equation:
model.x = C*(model.hess \ (model.hess' \ model.ss));
out = model.x'*K2; % Recompute the outputs...
new_sv_bool = (out<1);
new_sv = find(new_sv_bool);
% The set of errors has changed (and so the Hessian), so we update
% the Cholesky decomposition of the Hessian.
change=0;
for i=find(new_sv_bool>sv_bool)
model.hess = cholupdate(model.hess,sqrt(C)*K2(:,i),'+');
model.ss = model.ss+K2(:,i);
change=1;
end
for i=find(sv_bool>new_sv_bool)
model.hess = cholupdate(model.hess,sqrt(C)*K2(:,i),'-');
model.ss = model.ss-K2(:,i);
change=1;
end
% Compute the objective function (it is not needed by the algorithm)
% obj = 0.5* (norm(hess*x)^2 - 2*C*sum(out(new_sv)) + C*length(new_sv));
% fprintf(['\rNb basis = %d (%d), iter Newton = %d, Obj = %.2f, ' ...
% 'Nb errors = %d '],length(hess)-1,length(find(x))-1,iter,obj,length(sv));
if change==0
break;
end
model.sv = new_sv;
sv_bool=new_sv_bool;
end
end
model.numSV(model.iter)=numel(model.S);
if (mod(curr,model.step)==0)
fprintf('#%.0f SV:%5.2f(%d)\tAER:%5.2f\n', ...
ceil(curr/1000),numel(model.S)/curr*100,numel(model.S),model.aer(model.iter)*100);
end
end
model.beta = [model.x(2:end); zeros(numel(model.S)-(numel(model.x)-1),1)]';
model.b = model.x(1);