The Similarity metric
Ming Li, Xin Chen, Xin Li, Bin Ma and Paul M.B. Vitanyi
IEEE Transactions on Information Theory Volume To appear, 2004.

## Abstract

A new class of metrics appropriate for measuring effective similarity relations between sequences, say one type of similarity per metric, is studied. We propose a new normalized information distance'', based on the noncomputable notion of Kolmogorov complexity, and show that it minorizes every metric in the class (that is, it is universal in that it discovers all effective similarities). We demonstrate that it too is a metric and takes values in $[0,1]$; hence it may be called the {\em similarity metric}. This is a theory foundation for a new general practical tool. We give two distinctive applications in widely divergent areas (the experiments by necessity use just computable approximations to the target notions). First, we computationally compare whole mitochondrial genomes and infer their evolutionary history. This results in a first completely automatic computed whole mitochondrial phylogeny tree. Secondly, we give fully automatically computed language tree of 52 different language based on translated versions of the Universal Declaration of Human Rights''.