4

Hello Stack Exchange community,

I'm relatively confused on what to do in this scenario. I am running an experiment that retrieves data of interest and stores it as an array. Experimental conditions are slightly different, and for my specific application, it is important to measure heterogeneity of my data. I was asked to use a distance metric for my 2D histograms generated post data analysis.

However, there are a wide array of options available after doing a literature search. There is the "Earth Mover's Distance", the Jensen-Shannon metric (the square root of the Jesen-Shannon divergence value), Bhattacharyya distance, Minkowski distance, etc.

I understand that these distances are defined differently, quantitatively speaking, and thus have difference implications, but for my example, what seems to be an efficient metric at quantifying differences in histograms (i.e, getting to the end goal of assessing heterogeneity)?

Thank you

Trevor Bugh
  • 41
  • 1
  • 2

1 Answers1

2

There are two other metrics that reportedly work well with histograms:

  1. Chi-square distance $ \chi^2 (x,y)=\frac{1}{2} \sum _{i=1} ^{d} \frac {(x_i - y_i)^2} {x_i+y_i}$
  2. Histogram intersection kernel (similarity) $k(x,y)=\sum _{i=1} ^{d} \min (x_i,y_i)$

I used these in my PhD thesis for image-based localization indoors. The image descriptors were essentially histograms and these two measures were found to be useful.

Vladislavs Dovgalecs
  • 2,315
  • 15
  • 18