From Similarity to Distance: Axiom Set, Monotonic Transformations and Metric Determinacy

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Issue
Математика и физика. Mathematics & Physics. 2018 11 (3)
Authors
Znamenskij, Sergej V.
Contact information
Znamenskij, Sergej V.: Ailamazyan Program Systems Institute of RAS Peter the First Street 4, Veskovo village, Pereslavl area,Yaroslavl region, 152021 Russia;
Keywords
metric space; similarity axioms; similarity normalization; metric determinacy; longest common subsequence
Abstract

How to normalise similarity metric to a metric space for a clusterization? A new system of axioms describes the known generalizations of distance metrics and similarity metrics, the Pearson correlation coefficient and the cosine metrics. Equivalent definitions of order-preserving transformations of metrics (both monotonic and pivot-monotonic) are given in various terms. The metric definiteness of convex metric subspaces Rn and Z among the pivot-monotonic transformations is proved. Faster formulas for the monotonic normalization of metrics are discussed.

Pages
331–341
Paper at repository of SibFU
http://elib.sfu-kras.ru/handle/2311/71626