FastAMI -- a Monte Carlo Approach to the Adjustment for Chance in Clustering Comparison Metrics

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.Comment: Accepted at AAAI 202

Compressing dictionaries of strings

The aim of this work is to develop a data structure capable of storing a set of strings in a compressed way providing the facility to access and search by prefix any string in the set. The notion of string will be formally exposed in this work, but it is enough to think a string as a stream of characters or a variable length dat}. We will prove that the data structure devised in our work will be able to search prefixes of the stored strings in a very efficient way, hence giving a performant solution to one of the most discussed problem of our age. In the discussion of our data structure, particular emphasis will be given to both space and time efficiency and a tradeoff between these two will be constantly searched. To understand how much string based data structures are important, think about modern search engines and social networks; they must store and process continuously immense streams of data which are mainly strings, while the output of such processed data must be available in few milliseconds not to try the patience of the user. Space efficiency is one of the main concern in this kind of problem. In order to satisfy real-time latency bounds, the largest possible amount of data must be stored in the highest levels of the memory hierarchy. Moreover, data compression allows to save money because it reduces the amount of physical memory needed to store abstract data and this particularly important since storage is the main source of expenditure in modern systems