Fig. 1: Normalization can impact which labeling is preferred by a mutual information measure.
From: Normalized mutual information is a biased measure for classification and community detection
In this example 64 objects are split into four equally sized true groups g, denoted by their color. Against this ground truth, we compare two candidate labelings, c1 and c2. The standard unnormalized mutual information I0(c; g) of Eq. (5) reports that labeling c1 shares more bits of information with the ground truth than does c2. By definition, the asymmetrically normalized mutual information NMI(A) will always agree with the unnormalized measure, as in this example. The symmetrically normalized NMI(S), on the other hand, is biased in favor of simpler labelings, which makes it prefer labeling c2 in this case.
