Clustering is at the very core of machine learning, and its applications proliferate with the increasing availability of data. However, as datasets grow, comparing clusterings with an adjustment for chance becomes computationally difficult, preventing unbiased ground-truth comparisons and solution selection. We propose FastAMI, a Monte Carlo-based method to efficiently approximate the Adjusted Mutual Information (AMI) and extend it to the Standardized Mutual Information (SMI). The approach is compared with the exact calculation and a recently developed variant of the AMI based on pairwise permutations, using both synthetic and real data. In contrast to the exact calculation our method is fast enough to enable these adjusted information-theoretic comparisons for large datasets while maintaining considerably more accurate results than the pairwise approach.

翻译：聚类是机器学习的核心，随着数据可用性的增加，其应用也在不断扩展。然而，随着数据集规模的增长，在聚类比较中进行机会调整在计算上变得困难，阻碍了无偏的基准真相比较和解决方案选择。我们提出FastAMI，一种基于蒙特卡洛的方法，用于高效近似调整互信息（AMI）并将其扩展到标准化互信息（SMI）。通过合成数据和真实数据，该方法与精确计算以及基于成对排列的AMI近期变体进行了比较。与精确计算相比，我们的方法足够快，能够在大数据集上实现这些基于信息论调整的比较，同时保持比成对方法显著更准确的结果。