jwcarr · June 20, 2024 08:50
diff --git a/vi.py b/vi.py
 # Variation of information (VI)
 #
 # 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))
 # VI = 3.322 (maximum VI is log(N) = log(10) = 3.322)
	# Variation of information (VI)
	#
	# 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))
	# VI = 3.322 (maximum VI is log(N) = log(10) = 3.322)