Information Distance in Multiples

TL;DR

This paper extends the concept of information distance from pairs to multiples, analyzing its properties and practical approximation using compression algorithms for applications in pattern recognition and data mining.

Contribution

It introduces a theoretical framework for information distance in multiples and explores its properties, providing practical methods for approximation with real-world compression tools.

Findings

Analysis of maximal overlap and metricity in multiples

Demonstration of universality and minimal overlap properties

Validation of approximation methods using compression algorithms

Abstract

Information distance is a parameter-free similarity measure based on compression, used in pattern recognition, data mining, phylogeny, clustering, and classification. The notion of information distance is extended from pairs to multiples (finite lists). We study maximal overlap, metricity, universality, minimal overlap, additivity, and normalized information distance in multiples. We use the theoretical notion of Kolmogorov complexity which for practical purposes is approximated by the length of the compressed version of the file involved, using a real-world compression program. {\em Index Terms}-- Information distance, multiples, pattern recognition, data mining, similarity, Kolmogorov complexity