Improved mutual information measure for classification and community detection
This addresses a fundamental issue in evaluating classification algorithms and community detection methods, providing a more accurate measure for researchers and practitioners in machine learning and data analysis.
The authors identified that the standard mutual information measure used in classification and community detection omits a crucial term, leading to substantial errors under real-world conditions, and they corrected this error to define a mutual information that works in all cases.
The information theoretic quantity known as mutual information finds wide use in classification and community detection analyses to compare two classifications of the same set of objects into groups. In the context of classification algorithms, for instance, it is often used to compare discovered classes to known ground truth and hence to quantify algorithm performance. Here we argue that the standard mutual information, as commonly defined, omits a crucial term which can become large under real-world conditions, producing results that can be substantially in error. We demonstrate how to correct this error and define a mutual information that works in all cases. We discuss practical implementation of the new measure and give some example applications.