function?Xout?=?learn_coefficients?（A?Y?gamma?Xinit）
%?The?feature-sign?search?algorithm
%?L1-regularized?least?squares?problem?solver
%
%?This?code?solves?the?following?problem:
%?
%????minimize_s?0.5*||y?-?A*x||^2?+?gamma*||x||_1
%?
%?The?detail?of?the?algorithm?is?described?in?the?following?paper:
%?‘Efficient?Sparse?Codig?Algorithms‘?Honglak?Lee?Alexis?Battle?Rajat?Raina?Andrew?Y.?Ng?
%?Advances?in?Neural?Information?Processing?Systems?（NIPS）?19?2007
%
%?Written?by?Honglak?Lee?
%?Copyright?2007?by?Honglak?Lee?Alexis?Battle?Rajat?Raina?and?Andrew?Y.?Ng

warning（‘off‘?‘MATLAB:divideByZero‘）;

use_Xinit=?false;???????%judge?wheather?X?have?initial---Xinit?
if?exist（‘Xinit‘?‘var‘）
????use_Xinit=?true;????%?We?have?initial?Xinit?for?X
end

Xout=?zeros（size（A2）?size（Y2））;%?output?the?result?y=AX?
??????????????????????????????????%?y--k*NA--k*mX--m*N
AtA?=?A‘*A;???????????????????????%?A?is?preseted
AtY?=?A‘*Y;???????????????????????%?Y?also?presented

rankA?=?rank（AtA）;
%rankA?=?min（size（A1）-10?size（A2）-10）;%?X?must?be?sparse

for?i=1:size（Y2）%?each?column?of?Y?is?a?sample
%????if?mod（i?100）==0?fprintf（‘.‘）;?end?%fprintf（1?‘l1ls_featuresign:?%d/%d\r‘?i?size（Y2））;?end
????
????if?use_Xinit?%?We?have?Xinitused?it?
????????idx1?=?find（Xinit（:i）~=0）;??????%?find?nonzero?coefficients?ith?sample
????????maxn?=?min（length（idx1）?rankA）;?%?length（idx1）?is?the?number?of?nonzero?coefficients
????????xinit?=?zeros（size（Xinit（:i）））;?%?all?zeros
????????xinit（idx1（1:maxn））?=??Xinit（idx1（1:maxn）?i）;
????????[Xout（:i）?fobj]=?ls_featuresign_sub?（A?Y（:i）?AtA?AtY（:?i）?gamma?xinit）;
????else
????????[Xout（:i）?fobj]=?ls_featuresign_sub?（A?Y（:i）?AtA?AtY（:?i）?gamma）;
????end
end
fprintf（1?‘\n‘）;

warning（‘on‘?‘MATLAB:divideByZero‘）;

return;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


function?[x?fobj]?=?ls_featuresign_sub?（A?y?AtA?Aty?gamma?xinit）

[LM]?=?size（A）;?%?the?dimension?of?sample----L?the?number?of?atoms---M

rankA?=?rank（AtA）;
%rankA?=?min（size（A1）-10?size（A2）-10）;%?why??

%?Step?1:?Initialize
usexinit?=?false;
if?~exist（‘xinit‘?‘var‘）?||?isempty（xinit）?%?we?don‘t?have?xinit
????xinit=?[];
????x=?sparse（zeros（M1））;??????%?the?coefficients?all?zerosinitialize?x=0;
????theta=?sparse（zeros（M1））;??%?the?sign?of?xitheta=0;
????act=?sparse（zeros（M1））;????%?active?setactive?set={};
????allowZero?=?false;
else
????%?xinit?=?[];
????x=?sparse（xinit）;??????????%?init?xx=xinit;
????theta=?sparse（sign（x））;????%?thetai?is?the?sign?of?xi
????act=?sparse（abs（theta））;???%?nonzeros?coefficience
????usexinit?=?true;???????????%?use?init
????allowZero?=?true;
end

%fname_debug?=?sprintf（‘../tmp/fsdebug_%x.mat‘?datestr（now?30））;

fobj?=?fobj_featuresign（x?A?y?AtA?Aty?gamma）;%?objective?function‘s?value

ITERMAX=400;?????????????%?iteration
optimality1=false;????????%?check?opt

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2014-07-27?17:30??LRAE+SC\
?????文件????????1415??2014-07-27?17:30??LRAE+SC\LRSE_SC.m
?????文件?????????920??2014-07-27?17:28??LRAE+SC\SRCE_function.m
?????目錄???????????0??2014-07-27?17:13??LRAE+SC\inexact_alm_rpca\
?????文件????????6148??2009-10-31?23:23??LRAE+SC\inexact_alm_rpca\.DS_Store
?????目錄???????????0??2014-07-27?17:13??LRAE+SC\inexact_alm_rpca\PROPACK\
?????文件?????????202??1998-12-07?23:24??LRAE+SC\inexact_alm_rpca\PROPACK\Afunc.m
?????文件?????????224??1998-12-07?23:25??LRAE+SC\inexact_alm_rpca\PROPACK\AtAfunc.m
?????文件?????????232??1998-12-07?23:25??LRAE+SC\inexact_alm_rpca\PROPACK\Atransfunc.m
?????文件?????????293??1998-12-07?23:25??LRAE+SC\inexact_alm_rpca\PROPACK\Cfunc.m
?????文件?????????987??2009-07-02?14:28??LRAE+SC\inexact_alm_rpca\PROPACK\bdsqr.m
?????文件???????74546??2004-03-18?04:12??LRAE+SC\inexact_alm_rpca\PROPACK\bdsqr.mexglx
?????文件???????25208??2004-03-18?05:39??LRAE+SC\inexact_alm_rpca\PROPACK\bdsqr.mexsg
?????文件???????26109??2000-05-01?07:18??LRAE+SC\inexact_alm_rpca\PROPACK\bdsqr.mexsg64
?????文件???????95852??2000-05-26?08:14??LRAE+SC\inexact_alm_rpca\PROPACK\bdsqr.mexsol
?????文件???????55808??2009-03-14?16:23??LRAE+SC\inexact_alm_rpca\PROPACK\bdsqr.mexw32
?????文件????????2102??2004-03-18?03:41??LRAE+SC\inexact_alm_rpca\PROPACK\bdsqr_mex.c
?????文件????????1504??2000-05-29?17:52??LRAE+SC\inexact_alm_rpca\PROPACK\compute_int.m
?????文件?????????445??2004-03-18?03:28??LRAE+SC\inexact_alm_rpca\PROPACK\dbdqr.f
?????文件??????256353??1998-09-08?03:13??LRAE+SC\inexact_alm_rpca\PROPACK\helio.mat
?????文件????????3544??2000-05-27?07:45??LRAE+SC\inexact_alm_rpca\PROPACK\lanbpro.doc
?????文件???????19514??2000-06-08?08:27??LRAE+SC\inexact_alm_rpca\PROPACK\lanbpro.m
?????文件????????3544??2000-05-27?08:40??LRAE+SC\inexact_alm_rpca\PROPACK\lanbpro.txt
?????文件????????2522??2000-05-27?07:45??LRAE+SC\inexact_alm_rpca\PROPACK\laneig.doc
?????文件????????9695??2001-08-16?03:57??LRAE+SC\inexact_alm_rpca\PROPACK\laneig.m
?????文件????????2522??2000-05-27?08:40??LRAE+SC\inexact_alm_rpca\PROPACK\laneig.txt
?????文件????????3336??2000-05-27?07:46??LRAE+SC\inexact_alm_rpca\PROPACK\lanpro.doc
?????文件???????14762??2000-05-10?07:20??LRAE+SC\inexact_alm_rpca\PROPACK\lanpro.m
?????文件????????3336??2000-05-27?08:40??LRAE+SC\inexact_alm_rpca\PROPACK\lanpro.txt
?????文件????????2386??2000-05-27?07:46??LRAE+SC\inexact_alm_rpca\PROPACK\lansvd.doc
?????文件????????9307??2000-05-17?07:55??LRAE+SC\inexact_alm_rpca\PROPACK\lansvd.m
............此處省略27個文件信息