The similarity metric

Details The similarity metric The similarity metric

2001-11-20

arxiv.org/abs/cs/0111054v3

Computer Science

Computational Complexity

13 pages, LaTex, 5 figures, Part of this work appeared in Proc. 14th ACM-SIAM Symp. Discrete Algorithms, 2003. This is the fin

Scientific paper

A new class of distances appropriate for measuring similarity relations between sequences, say one type of similarity per distance, is studied. We propose a new ``normalized information distance'', based on the noncomputable notion of Kolmogorov complexity, and show that it is in this class and it minorizes every computable distance in the class (that is, it is universal in that it discovers all computable similarities). We demonstrate that it is a metric and call it the {\em similarity metric}. This theory forms the foundation for a new practical tool. To evidence generality and robustness we give two distinctive applications in widely divergent areas using standard compression programs like gzip and GenCompress. First, we compare whole mitochondrial genomes and infer their evolutionary history. This results in a first completely automatic computed whole mitochondrial phylogeny tree. Secondly, we fully automatically compute the language tree of 52 different languages.

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