cluster_sim.py

#!/usr/bin/env python3

"""Compute pair-wise cluster-level comparison metrics

These metrics are taken from:
https://www.cs.umd.edu/class/spring2012/cmsc828L/Papers/MenestrinaVLDB10.pdf"""

import random
from string import ascii_lowercase as alphabet
from math import sqrt, log
from itertools import combinations, product, chain

def partition(items, seed=None):
    shuffled = [item for item in items]
    if seed:
        random.seed(seed)
    random.shuffle(shuffled)
    cell = []
    while shuffled:
        while random.randint(0, 1):
            if shuffled:
                cell.append(shuffled.pop())
        if cell:
            yield tuple(cell)
        cell = []

def universe(*clusters):
    return set(chain(*chain(*clusters)))

def intersection(*args):
    return set.intersection(*({tuple(x) for x in arg} for arg in args))

def k(r, s):
    """Compute pair-wise cluster-level comparison metric K"""
    author_purities = []
    cluster_purities = []
    n = float(len(universe(r, s)))
    for x, y in product(r, s):
        numerator = float(len(intersection(x, y)) ** 2)
        author_purities.append(numerator / float(len(x)))
        cluster_purities.append(numerator / float(len(y)))
    average_author_purities = sum(author_purities) / n
    average_cluster_purities = sum(cluster_purities) / n
    return sqrt(average_author_purities * average_cluster_purities)

def entropy(r, n):
    return -1 * sum(len(x) / n * log(len(x) / n, 2) for x in r)

def information(r, s, n):
    i = 0.0
    for pair in product(r, s):
        x, y = map(set, pair)
        overlap = len(intersection(x, y))
        if overlap > 0:
            i += (overlap / n) * log((overlap * n) / (len(x) * len(y)), 2)
    return i

def vi(r, s):
    """Compute the pair-wise Variation of Information (VI)"""
    n = float(len(universe(r, s)))
    return entropy(r, n) + entropy(s, n) - (2 * information(r, s, n))

def demo(r, s):
    print('R:', *list(sorted(x) for x in sorted(r)), sep=', ')
    print('S:', *list(sorted(x) for x in sorted(s)), sep=', ')
    print('K(R,S):', k(r, s))
    print('VI(R,S):', vi(r, s))

if __name__ == '__main__':
    a, b, c, d = 'abcd'
    r = (a, b), (c,), (d,)
    s = (a, b), (c, d)
    demo(r, s)
    #partitions = [tuple(partition(alphabet, seed)) for seed in alphabet]
    #for r, s in combinations(partitions, 2):
    #    demo(r, s)