The information theoretic measure known as mutual information is widely used as a way to quantify the similarity of two different labelings or divisions of the same set of objects, such as arises for instance in clustering and classification problems in machine learning or community detection problems in network science. 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 derive an expression for this missing term and hence write a corrected mutual information that gives accurate results even in cases where the standard measure fails. We discuss practical implementation of the new measure and give example applications.

中文翻译：

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改进了用于聚类，分类和社区检测的互信息度量

被称为互信息的信息理论量度被广泛用作量化同一组对象的两个不同标签或划分的相似性的方法，例如在机器学习中的聚类和分类问题或网络中的社区检测问题中出现的情况科学。在这里，我们认为，通常定义的标准互信息忽略了一个关键术语，该术语在现实世界中可能会变得很大，从而产生可能存在重大错误的结果。我们导出了该缺失项的表达式，因此编写了正确的互信息，即使在标准度量失败的情况下也能提供准确的结果。我们讨论了新措施的实际实施，并给出了示例应用程序。