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function z = mutualInformation(x, y)
% Compute mutual information I(x,y) of two discrete variables x and y.
% Written by Mo Chen (mochen80@gmail.com).
assert(numel(x) == numel(y));
n = numel(x);
x = reshape(x,1,n);
y = reshape(y,1,n);
l = min(min(x),min(y));
x = x-l+1;
y = y-l+1;
k = max(max(x),max(y));
idx = 1:n;
Mx = sparse(idx,x,1,n,k,n);
My = sparse(idx,y,1,n,k,n);
Pxy = nonzeros(Mx'*My/n); %joint distribution of x and y
Hxy = -dot(Pxy,log2(Pxy+eps));
Px = mean(Mx,1);
Py = mean(My,1);
% entropy of Py and Px
Hx = -dot(Px,log2(Px+eps));
Hy = -dot(Py,log2(Py+eps));
% mutual information
z = Hx + Hy - Hxy;
endfunction |
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