Journal of Siberian Federal University. Mathematics & Physics: From Similarity to Distance / Axiom Set, Monotonic Transformations and Metric Determinacy

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Journal of Siberian Federal University. Mathematics & Physics: 2018, Vol. 11, Issue 3
Znamenskij, Sergej V.
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Znamenskij, Sergej V.: Ailamazyan Program Systems Institute of RAS Peter the First Street 4, Veskovo village, Pereslavl area,Yaroslavl region, 152021 Russia;
metric space; similarity axioms; similarity normalization; metric determinacy; longest common subsequence

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.

Paper at repository of SibFU