function?F=carspls（XyAfoldmethodnum）?
%+++?CARS:?Competitive?Adaptive?Reweighted?Sampling?method?for?variable?selection.
%+++?X:?The?data?matrix?of?size?m?x?p
%+++?y:?The?reponse?vector?of?size?m?x?1
%+++?A:?the?maximal?principle?to?extract.
%+++?fold:?the?group?number?for?cross?validation.
%+++?num:?the??number?of?Monte?Carlo?Sampling?runs.
%+++?method:?pretreatment?method.
%+++?Hongdong?Li?Dec.15?2008.
%+++?Advisor:?Yizeng?Liang?yizeng_liang@263.net
%+++?lhdcsu@gmail.com
%+++?Ref:??Hongdong?Li?Yizeng?Liang?Qingsong?Xu?Dongsheng?Cao?Key
%????wavelengths?screening?using?competitive?adaptive?reweighted?sampling?
%????method?for?multivariate?calibration?Anal?Chim?Acta?2009?648（1）:77-84


tic;
%+++?Initial?settings.
if?nargin<6;num=50;end;
if?nargin<5;method=‘center‘;end;
if?nargin<4;fold=5;end;
if?nargin<3;A=2;end;

%+++?Initial?settings.
[MxNx]=size（X）;
A=min（[Mx?Nx?A]）;
index=1:Nx;
ratio=0.9;
r0=1;
r1=2/Nx;
Vsel=1:Nx;
Q=floor（Mx*ratio）;
W=zeros（Nxnum）;
Ratio=zeros（1num）;

%+++?Parameter?of?exponentially?decreasing?function.?
b=log（r0/r1）/（num-1）;??a=r0*exp（b）;

%+++?Main?Loop
for?iter=1:num
?????
?????perm=randperm（Mx）;???
?????Xcal=X（perm（1:Q）:）;?ycal=y（perm（1:Q））;???%+++?Monte-Carlo?Sampling.
?????
?????PLS=pls（Xcal（:Vsel）ycalAmethod）;????%+++?PLS?model
?????w=zeros（Nx1）;coef=PLS.coef_origin（1:end-1end）;
?????w（Vsel）=coef;W（:iter）=w;?
?????w=abs（w）;??????????????????????????????????%+++?weights
?????[wsindexw]=sort（-w）;??????????????????????%+++?sort?weights
?????
?????ratio=a*exp（-b*（iter+1））;??????????????????????%+++?Ratio?of?retained?variables.
?????Ratio（iter）=ratio;
?????K=round（Nx*ratio）;??
?????
?????
?????w（indexw（K+1:end））=0;??????????????????????%+++?Eliminate?some?variables?with?small?coefficients.??
?????
?????Vsel=randsample（NxNxtruew）;?????????????????%+++?Reweighted?Sampling?from?the?pool?of?retained?variables.?????????????????
?????Vsel=unique（Vsel）;??????????????
?????fprintf（‘The?%dth?variable?sampling?finished.\n‘iter）;????%+++?Screen?output.
?end

%+++??Cross-Validation?to?choose?an?optimal?subset;
RMSEP=zeros（1num）;
Q2_max=zeros（1num）;
Rpc=zeros（1num）;
for?i=1:num
???vsel=find（W（:i）~=0）;
?
???CV=plscvfold（X（:vsel）yAfoldmethod0）;??
???RMSEP（i）=CV.RMSECV;
???Q2_max（i）=CV.Q2_max;???
???
???Rpc（i）=CV.optPC;
???fprintf（‘The?%d/%dth?subset?finished.\n‘inum）;
end
[RminindexOPT]=min（RMSEP）;
Q2_max=max（Q2_max）;




%+++?save?results;
time=toc;
%+++?output
F.W=W;
F.time=time;
F.cv=RMSEP;
F.Q2_max=Q2_max;
F.minRMSECV=Rmin;
F.iterOPT=indexOPT;
F.optPC=Rpc（indexOPT）;
Ft.ratio=Ratio;
F.vsel=find（W（:indexOPT）~=0）‘;



function?sel=weightsampling_in（w）
%Bootstrap?sampling
%2007.9.6H.D.?Li.

w=w/sum（w）;
N1=length（w）;
min_sec（1）=0;?max_sec（1）=w（1）;
for?j=2:N1
???max_sec（j）=sum（w（1:j））;
???min_sec（j）=sum（w（1:j-1））;
end
%?figure;plot（max_sec‘r‘）;hold?on;plot（min_sec）;
??????
for?i=1:N1
??

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????3796??2014-11-18?15:43??Functions\Data?processing.m
?????文件????????3401??2014-03-06?17:18??Functions\carspls.m
?????文件????????1936??2014-03-10?15:03??Functions\deriv.m
?????文件?????????955??2014-03-06?17:20??Functions\genfact.m
?????文件????????1146??2014-03-06?17:20??Functions\grampoly.m
?????文件????????3472??2014-11-12?22:07??Functions\ks.m
?????文件????????3038??2014-03-06?17:18??Functions\mcs.m
?????文件????????2311??2014-03-06?17:19??Functions\msc.m
?????文件????????1950??2014-11-11?19:32??Functions\pls.m
?????文件????????1728??2014-03-06?17:18??Functions\pls_nipals.m
?????文件????????2720??2014-11-11?19:36??Functions\plscvfold.m
?????文件?????????790??2014-03-06?17:18??Functions\pretreat.m
?????文件????????2561??2014-06-03?14:45??Functions\smooth.m
?????文件?????????918??2014-11-06?17:28??Functions\snv.m
?????文件?????????451??2014-03-06?17:18??Functions\tp.m
?????文件????????1218??2014-03-06?17:20??Functions\weight.m
?????文件????????1312??2014-11-18?02:51??license.txt