Suppose that you have +/- elements aggregated into a weighted distribution function that represents some deviation from an unknown background distribution. What would be a good similarity metric for comparing two such distributions (2D or 3D), if they each represent different perturbations from different backgrounds? In a simple case where the distribution is known, I was looking into Kullback-Leibler divergence, earth mover's distance, or Bhattacharyya distance, but I would first need to first consider how to properly extend them to handle this problem (if it makes sense). Alternatively, I could just integrate their difference. What do you all think?