function?[?I1?I2?]?=?KraskovMI（?X?Y?k?varargin?）
%KraskovMI?computes?the?Kraskov?estimator?for?the?mutual?information.
%???1.?Input:?X?Y
%?????????????k:?nearest?neighbour
%?????????????zeroFix?（optional）:?fix?the?negative?estimation?to?0?（default
%?????????????????????????????????false）;
%
%???univariate:?X?Y?（n?x?1）?vector
%???multivariate:?X?Y?（n?x?m）?matrix?（rows=observations
%???columns=variables）
%
%???2.?Output:?I1?I2:?the?two?estimator?of?MI?I（1）?I（2）?（see?Ref.）
%
%?Ref:?Kraskov?Alexander?Harald?St鰃bauer?and?Peter?Grassberger.
%??????“Estimating?mutual?information.“?Physical?review?E?69.6?（2004）:?066138.
%
%?Author:?Paolo?Inglese?
%?Last?revision:?17-05-2015

if?nargin??4
????error（‘Wrong?input?number.‘）;
end
if?nargin?==?3
????zeroFix?=?false;
end
if?nargin?==?4
????if?~islogical（varargin{1}）
????????error（‘zeroFix?must?be?true?or?false‘）;
????else
????????zeroFix?=?varargin{1};
????end
end
????

if?size（X?1）?~=?size（Y?1）
????error（‘X?and?Y?must?contain?the?same?number?of?samples‘）;
end

nObs?=?size（X?1）;

%?compute?distance?between?each?sample?and?its?k-th?nearest?neighbour
dz?=?zeros（nObs?nObs）;
dx?=?zeros（nObs?nObs）;
dy?=?zeros（nObs?nObs）;
for?i?=?1:nObs
????for?j?=?1:nObs
????????dx（ij）?=?sqrt（sum（（X（i?:）?-?X（j?:））.^2））;
????????dy（ij）?=?sqrt（sum（（Y（i?:）?-?Y（j?:））.^2））;
????????dz（ij）?=?max（[dx（i?j）?dy（i?j）]）;
????end
end

%?find?nx（i）?and?ny（i）
Eps?=?zeros（nObs?1）;
Nn?=?zeros（nObs?1）;

nx1?=?zeros（nObs?1）;
ny1?=?zeros（nObs?1）;
nx2?=?zeros（nObs?1）;
ny2?=?zeros（nObs?1）;
for?i?=?1:nObs
????
????dxSample?=?dx（i?:）;
????dxSample（i）?=?[];
????
????dySample?=?dy（i?:）;
????dySample（i）?=?[];
????
????dzSample?=?dz（i?:）;
????dzSample（i）?=?[];
????[EpsSample?NnSample]?=?sort（dzSample?‘ascend‘）;
????Eps（i）?=?EpsSample（k）;
????Nn（i）?=?NnSample（k）;
????
????nx1（i）?=?sum（dxSample?????ny1（i）?=?sum（dySample?????
????nx2（i）?=?sum（dxSample?<=?Eps（i））;
????ny2（i）?=?sum（dySample?<=?Eps（i））;
????
end

%?mutual?information?estimators
I1?=?psi（k）?-?sum（psi（nx1?+?1）?+?psi（ny1?+?1））?/?nObs?+?psi（nObs）;
I2?=?psi（k）?-?1/k?-?sum（psi（nx2）?+?psi（ny2））?/?nObs?+?psi（nObs）;

if?（zeroFix）
????if?I1?????????warning（‘First?estimator?is?negative?->?0‘）;
????????I1?=?0;
????end
????if?I2?????????warning（‘Second?estimator?is?negative?->?0‘）;
????????I2?=?0;
????end
end

end

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

?????文件???????5843??2004-06-04?04:01??互信息1\1ICAtests.C

?????文件???????2766??2004-06-04?10:23??互信息1\ICAtests.m

?????文件????????502??2005-11-23?14:34??互信息1\makefile

?????文件????????286??2005-09-26?21:36??互信息1\mamari.m

?????文件???????7918??2004-06-04?04:00??互信息1\MIClustering.C

?????文件????????819??2004-06-04?10:23??互信息1\MIClustering.m

?????文件???????3254??2004-06-04?03:59??互信息1\MIhigherdim.C

?????文件????????882??2004-06-04?10:23??互信息1\MIhigherdim.m

?????文件???????9370??2004-06-04?04:17??互信息1\milca.C

?????文件???????1505??2018-01-20?23:03??互信息1\milca.m

?????文件??????10459??2005-11-23?14:32??互信息1\milcadelay.C

?????文件??????84992??2005-11-23?15:25??互信息1\milcadelay.exe

?????文件???????1872??2004-06-04?10:23??互信息1\milcadelay.m

?????文件?????320832??2004-06-04?10:23??互信息1\milcaECG8ch.mat

?????文件??????60784??2004-06-04?04:13??互信息1\miutils.C

?????文件???????7957??2004-06-04?03:21??互信息1\miutils.h

?????文件???????3417??2004-06-04?04:00??互信息1\MIxnyn.C

?????文件????????900??2004-06-04?10:23??互信息1\MIxnyn.m

?????文件???????6185??2004-06-04?10:23??互信息1\Tutorial.m

?????文件???????1034??2006-01-06?11:29??互信息2\mi\condentropy.m

?????文件???????1237??2006-01-06?11:29??互信息2\mi\condmutualinfo.m

?????文件????????724??2006-01-06?11:29??互信息2\mi\demo_mi.m

?????文件????????477??2007-08-23?09:49??互信息2\mi\elementmexheader.h

?????文件????????761??2006-01-06?11:29??互信息2\mi\entropy.m

?????文件???????1800??2006-01-06?11:29??互信息2\mi\estcondentropy.cpp

?????文件??????40960??2006-01-06?11:29??互信息2\mi\estcondentropy.dll.old

?????文件???????8901??2006-01-06?11:29??互信息2\mi\estcondentropy.mexglx

?????文件??????54608??2007-08-23?09:49??互信息2\mi\estcondentropy.mexmac

?????文件??????20480??2009-04-18?17:58??互信息2\mi\estcondentropy.mexw32

?????文件???????1249??2006-01-06?11:29??互信息2\mi\estentropy.cpp

............此處省略97個文件信息