Variation of information (VI)
October 2, 2017 ยท View on GitHub
Meila, M. (2007). Comparing clusterings-an information
based distance. Journal of Multivariate Analysis, 98,
873-895. doi:10.1016/j.jmva.2006.11.013
https://en.wikipedia.org/wiki/Variation_of_information
from math import log
def variation_of_information(X, Y): n = float(sum([len(x) for x in X])) sigma = 0.0 for x in X: p = len(x) / n for y in Y: q = len(y) / n r = len(set(x) & set(y)) / n if r > 0.0: sigma += r * (log(r / p, 2) + log(r / q, 2)) return abs(sigma)
Identical partitions
X1 = [ [1,2,3,4,5], [6,7,8,9,10] ] Y1 = [ [1,2,3,4,5], [6,7,8,9,10] ] print(variation_of_information(X1, Y1))
VI = 0
Similar partitions
X2 = [ [1,2,3,4], [5,6,7,8,9,10] ] Y2 = [ [1,2,3,4,5,6], [7,8,9,10] ] print(variation_of_information(X2, Y2))
VI = 1.102
Dissimilar partitions
X3 = [ [1,2], [3,4,5], [6,7,8], [9,10] ] Y3 = [ [10,2,3], [4,5,6,7], [8,9,1] ] print(variation_of_information(X3, Y3))
VI = 2.302
Totally different partitions
X4 = [ [1,2,3,4,5,6,7,8,9,10] ] Y4 = [ [1], [2], [3], [4], [5], [6], [7], [8], [9], [10] ] print(variation_of_information(X4, Y4))