function?[?I1?I2?]?=?KraskovMI（?X?Y?k?varargin?）
%KraskovMI?computes?the?Kraskov?estimator?for?the?mutual?information.
%???1.?Input:?X?Y?（n?x?1）?vectors
%?????????????k:?nearest?neighbour
%?????????????zeroFix?（optional）:?fix?the?negative?estimation?to?0?（default
%?????????????????????????????????false）;
%
%???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）?=?pdist（[X（i?:）;?X（j?:）]）;
????????dy（ij）?=?pdist（[Y（i?:）;?Y（j?:）]）;
????????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????????2376??2015-05-17?07:23??K近鄰互信息計算程序\KraskovMI.m
?????文件????????1313??2015-05-17?07:23??K近鄰互信息計算程序\license.txt
?????目錄???????????0??2018-09-17?19:42??K近鄰互信息計算程序\