Normalized Mutual Information

Problem

Compute the normalized mutual information between two label lists in bits: NMI = 2 * MI / (H(a) + H(b)), where MI uses joint and marginal probabilities and H is Shannon entropy base 2.

Return 0.0 if the entropies sum to 0 or the input is empty.

Hint

Normalizing by the average entropy keeps NMI between 0 and 1.

Test cases

case 1

in: [[0,0,1,1],[0,0,1,1]]

expected: 1

case 2

in: [[0,1,0,1],[0,0,1,1]]

expected: 0

case 3

in: [[0,0,1,1],[0,1,1,1]]

expected: 0.34371101848545077

case 4

in: [[],[]]

expected: 0

Starter codePython

import math
def normalized_mutual_information(a, b):
    # Your code here
    pass

4 test cases · run your code against them in the editor