I've been working on a statistical learning problem and seem to have hit a roadblock. It's basically regarding somehow measuring how randomized or unsorted a given vector is, with respect to a reference vector.
E.g if the reference vector has 5 elements of the orientation: X = ABCDE, then is there a function that could return a score s for some Y = BDCAE with respect to X?
i.e Something like: f(ABCDE, ABCDE) = 0 (or 1)
f(BDCAE , ABCDE) = s
In case there is some straightforward way to do it, could you kindly let me know if we can have weight for each element as well, as in {A: w1, B: w2, ....}?
Thank you in advance.
Is the Kendall Tau distance close to what you need?
http://en.wikipedia.org/wiki/Kendall_tau_distance