  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.
