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.

翻译：归一化互信息被广泛用作评估聚类与分类算法性能的相似性度量。本文指出，归一化互信息返回的结果存在偏差，其原因有二：首先，该方法忽略了列联表的信息量；其次，其对称归一化过程会引入对算法输出的虚假依赖性。我们提出一种改进的互信息计算方法，可同时修正这两项缺陷。为实证使用无偏度量标准的重要性，我们对网络社区检测领域的一系列常用算法进行了大量数值测试，结果表明传统互信息的偏差会显著影响关于最优算法的判定结论。