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The similarity metric | | Ming Li
; Xin Chen
; Xin Li
; Bin Ma
; Paul Vitanyi
; | | Date: |
20 Nov 2001 | | Subject: | Computational Complexity; Computational Engineering, Finance, and Science; Metric Geometry; Combinatorics; Data Analysis, Statistics and Probability; Statistical Mechanics ACM-class: J.3, E.4 | cs.CC cond-mat.stat-mech cs.CE math.CO math.MG physics.data-an | | Affiliation: | Univ. of Waterloo and BioInformatics Solutions Inc.), Xin Chen (Univ. California, Santa Barbara), Xin Li (Univ. Western Ontario), Bin Ma (Univ. Western Ontario), Paul Vitanyi (CWI and Univ. of Amsterdam | | Abstract: | 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. | | Source: | arXiv, cs.CC/0111054 | | Services: | Forum | Review | PDF | Favorites | |
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