%?Using?pegasos?algorithm?to?solve?a?simple?linear?SVM?classifier?without?a?bias?term?（b）
%?Note?that?we?use?CVX?libarary?to?first?optimal?value?and?then?report?the
%?convergence?rate?for?pegasos?algorithm

clear;
clc;

%?load?data
load?q1x.dat
load?q1y.dat

%?load?a9a_X.mat;
%?load?a9a_Y.mat;
tic;
%?define?variables

?X?=?q1x;
?Y?=?2*（q1y-0.5）;%-11

%??X?=?X1;
%??Y?=?ttrain‘;%-11


[train_num?feature_num]?=?size（X）;


lambda?=?0.01;?%?it?can?be?set?as?1/C
cvx_begin?quiet
????variable?w（feature_num）;
????variable?xi（train_num）;
?%minimize?1/2*lambda?||?x?||^2?+?1/k*sigma（max{01-yw‘x}）
????minimize（?0.5*lambda*w‘*w?+?（1?/?train_num）?*sum（xi））;
????subject?to
????????Y?.*?（X*w）?>=?1?-?xi;
????????xi?>=?0;
cvx_end

fbest?=?cvx_optval;

maxIter?=?5000;
[w?fval]?=?pegasos（XYlambda[]maxIter10）;
toc;
%?reporting?accuracy
t_num?=?sum（sign（X?*?w）?==?Y）;
accuracy?=?100?*?t_num?/?train_num;
fprintf（‘Accuracy?on?training?set?is?%.4f?%%\n‘?accuracy）;

%?plot?convergence?rate
figure（1）?clf
step?=?100;
semilogy（?1:step:maxIter?fval（1:step:end）?-?fbest?‘r-.‘‘LineWidth‘1.5?）;
xlabel（‘#?iter‘）;
ylabel（‘f?-?fmin‘）;
axis（[1?maxIter?1e-8?2e2]）;
title（‘Convergence?rate?for?pegasos?algorithm‘）;

%?visualize
figure（2）?clf
xp?=?linspace（min（X（:1））?max（X（:1））?100）;
yp?=?-?w（1）?*?xp?/?w（2）;
yp1?=?-?（w（1）*xp?-?1）?/?w（2）;?%?margin?boundary?for?support?vectors?for?y=1
yp0?=?-?（w（1）*xp?+?1）?/?w（2）;?%?margin?boundary?for?support?vectors?for?y=0

%?index?of?negative?samples
?idx0?=?find（q1y==0）;
%??idx0?=?find（Y==0）;
%?index?of?positive?samples
?idx1?=?find（q1y==1）;
%??idx1?=?find（Y==1）;

plot（X（idx0?1）?X（idx0?2）?‘rx‘）;?
hold?on
plot（X（idx1?1）?X（idx1?2）?‘go‘）;
plot（xp?yp?‘-b‘?xp?yp1?‘--g‘?xp?yp0?‘--r‘）;
hold?off
title（sprintf（‘decision?boundary?for?a?linear?SVM?classifier?with?lambda?=?%g‘?lambda））;

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件?????252892??2015-11-20?10:42??pegasos\a9a_X.mat

?????文件???????6165??2015-11-20?10:42??pegasos\a9a_Y.mat

????.......??????2365??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\abs.m

????.......??????1096??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\blkdiag.m

????.......??????1551??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\builtins.m

????.......??????2240??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\cat.m

????.......???????455??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\conj.m

????.......??????2140??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\conv.m

????.......???????803??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\ctranspose.m

????.......??????2816??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\cumprod.m

????.......??????1844??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\cumsum.m

????.......??????1112??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\diag.m

????.......???????438??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\disp.m

????.......???????532??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\end.m

????.......???????754??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\eq.m

????.......??????3398??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\exp.m

????.......??????1484??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\find.m

????.......???????368??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\full.m

????.......??????1224??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\ge.m

????.......??????1448??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\gt.m

????.......??????1289??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\hankel.m

????.......???????225??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\horzcat.m

????.......???????519??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\imag.m

????.......???????725??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\ipermute.m

????.......???????607??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\isreal.m

????.......??????1398??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\kron.m

????.......???????932??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\ldivide.m

????.......??????1269??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\le.m

????.......??????4070??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\log.m

????.......??????1493??2015-06-11?09:43??pegasos\cvx\builtins\@cvx\lt.m

............此處省略1404個文件信息