# KL divergence or similar “distance” metric between two multivariate distributions

I have a large dataset composed of many samples; each sample is as follows:

• imagine a grid indexed by i,j
• for a sample k, I have Y_k, where Y_k(i,j) is the probability density for k at (i,j)
• of course, summing the entire grid (each cell in the grid) yields 1

I have many (~100 for now) such samples, with different probability distributions over the exact same fixed grid. The distributions don't follow any parametric model, as far as I can tell.

My question is: I would like to compute all vs. all "distances" between these distributions. The goal is to feed the distances into a clustering algorithm, etc to figure out the general "classes" of distributions .... although they are all different from each other, just looking at them visually I see that there is clear grouping....of course it would nice to be able to do this algorithmically for scale, etc.