Authors: Russell Leidich
The Jensen-Shannon divergence (JSD) quantifies the “information distance” between a pair of probability distributions. (A more generalized version, which is beyond the scope of this paper, is given in . It extends this divergence to arbitrarily many such distributions. Related divergences are presented in , which is an excellent summary of existing work.)
A couple of novel applications for this divergence are presented herein, both of which involving sets of whole numbers constrained by some nonzero maximum value. (We’re primarily concerned with discrete applications of the JSD, although it’s defined for analog variables.) The first of these, which we can call the “Jensen-Shannon divergence transform” (JSDT), involves a sliding “sweep window” whose JSD with respect to some fixed “needle” is evaluated at each step as said window moves from left to right across a superset called a “haystack”.
The second such application, which we can call the “Jensen-Shannon exodivergence transform” (JSET), measures the JSD between a sweep window and an “exosweep”, that is, the haystack minus said window, at all possible locations of the latter. The JSET turns out to be exceptionally good at detecting anomalous contiguous subsets of a larger set of whole numbers.
We then investigate and attempt to improve upon the shortcomings of the JSD and the related Kullback-Leibler divergence (KLD).
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