MutualInfo.zip_mutual information_mutualinfo_互信息_互信息的计算_计算互信息

function [Ixy,lambda]=MutualInfo(X,Y) %% % Estimating Mutual Information with Moon et al. 1995 % between X and Y % Input parameter % X and Y : data column vectors (nL*1, nL is the record length) % % Output % Ixy : Mutual Information % lambda: scaled mutual information similar comparabble to % cross-correlation coefficient % % Programmed by % Taesam Lee, Ph.D., Research Associate % INRS-ETE, Quebecc % Hydrologist % Oct. 2010 % % X=X'; Y=Y'; d=2; nx=length(X); hx=(4/(d+2))^(1/(d+4))*nx^(-1/(d+4)); Xall=[X;Y]; sum1=0; for is=1:nx pxy=p_mkde([X(is),Y(is)]',Xall,hx); px=p_mkde([X(is)],X,hx); py=p_mkde([Y(is)],Y,hx); sum1=sum1+log(pxy/(px*py)); end Ixy=sum1/nx; lambda=sqrt(1-exp(-2*Ixy)); %% Multivariate kernel density estimate using a normal kernel % with the same h % input data X : dim * number of records % x : the data point in order to estimate mkde (d*1) vector % h : smoothing parameter function [pxy]=p_mkde(x,X,h); s1=size(X); d=s1(1); N=s1(2); Sxy=cov(X'); sum=0; %p1=1/sqrt((2*pi)^d*det(Sxy))*1/(N*h^d); % invS=inv(Sxy); detS=det(Sxy); for ix=1:N p2=(x-X(:,ix))'*(Sxy^(-1))*(x-X(:,ix)); sum=sum+1/sqrt((2*pi)^d*detS)*exp(-p2/(2*h^2)); end pxy=1/(N*h^d)*sum; %% Reference % Moon, Y. I., B. Rajagopalan, and U. Lall (1995), % Estimation of Mutual Information Using Kernel Density Estimators, % Phys Rev E, 52(3), 2318-2321.