JuliaStats/Distance.jl — pull request #19 by wildart (2014-06-08 22:41:47+00:00)
Title: histogram intersection distance

Histogram intersection distance: HID(a,b) = 1 - Σₜmin(aₜ, bₜ)/Σₜbₜ. It is used for partial histogram matching.

It is a variation of [Earth mover's distance](http://en.wikipedia.org/wiki/Earth_mover%27s_distance) with histogram intersection kernel, K(a,b) = Σₜmin(aₜ, bₜ). If using only kernel for calculating distance then positive definiteness does not hold, d(x,x)≠0. So, trick with 1-(normalized kernel value) is used. In its turn, normalization brakes symmetry axiom, d(x,y)≠d(y,x), because of the dependency on one of the parameters. So, it is not a proper metric, even though triangle inequality property is satisfied.