MATLAB's custom distance function example for two matrices.

How does MATLAB's @distfun work for two matrices. Suppose:

X1 = rand(5);
X2 = rand(3);

How to compute the KL-Divergence between X1 and X2 using @distfun? I do not see any non trivial distance example in manual. Please advise.

[Viren Gupta]

I checked the documentation of @distfun here and it says that if Z1 and Z2 are 2 inputs to the function, then Z1 need to have a single row.

Apart from this how are you trying to find KL divergence between 2 vectors of different length?

[hello_world]

@Viren Gupta: I also followed document and trivial example given there. Can you show me a working example for non trivial cases, such as, KL Divergence which depends on two probability distributions P and Q. So, you may generate two random distributions.

Answer 1

[Viren Gupta]

Here is a working example if you want to find KL divergence between 2 vectors.

z1=rand(1,5);
z2=rand(1,5);

X=[z1;z2];
fn=@distfun;
d=pdist(X,fn);
function f = distfun(x1,x2)
    l=size(x1,2);
    KL=0;
    for i=1:l
        KL=KL+x2(i)*log(x2(i)/x1(i));
    end
    f=KL;
end

Hope this helps.