Normalized mutual information is a biased measure for classification and community detection

Normalized mutual information is widely used as a similarity measure for evaluating the performance of clustering and classification algorithms. In this paper, we argue that results returned by the normalized mutual information are biased for two reasons: first, because they ignore the information content of the contingency table and, second, because their symmetric normalization introduces spurious dependence on algorithm output. We introduce a modified version of the mutual information that remedies both of these shortcomings. As a practical demonstration of the importance of using an unbiased measure, we perform extensive numerical tests on a basket of popular algorithms for network community detection and show that one’s conclusions about which algorithm is best are significantly affected by the biases in the traditional mutual information. From blood tests to friend groups, normalized mutual information is widely used to assess similarity between classifications, outcomes, or labelings of data. Here the authors demonstrate systematic biases of this measure and propose a modification that eliminates them.