Generalized (alpha-) Jensen-Shannon-divergence Example script to calculate the JSD between two probability distributions.

Background

The generalized Jensen-Shannon-divergence measures the distance between two probability distribution. It is a generalization of the 'normal' Jensen-Shannon-divergence using the generalized entropy of order alpha.

More background can be found here:

Martin Gerlach, Francesc Font-Clos, and Eduardo G. Altmann, Similarity of Symbol Frequency Distributions with Heavy Tails, Physical Review X 6 (2016) 021009 https://journals.aps.org/prx/abstract/10.1103/PhysRevX.6.021009

Running

Simply run

python run_jsda.py

Arguments

-f1: word-count file #1

-f2: word-count file #2

-a: set the alpha-exponent in the JSD (default:1 = normal JSD)

-n: get the normalized version of the JSD (default: False)

-w: whether the two distributions should be weights according to size (default: False)

-s: calculate expected JSD from random null model from s random realizations (default: s=0 )

Data

The data are the counts of words from two books of the Project Gutenberg corpus.

• data/PG299_counts.txt
• data/PG304_counts.txt

where each line corresponds to the number of times a word occurs in that book

word \t count \n

Requirements:

• python
• numpy
• jupyer/matplotlib for the example-notebook