From Similarity to Distance: Axiom Set, Monotonic Transformations and Metric Determinacy
Znamenskij Sergej V. · Journal of Siberian Federal University Mathematics & Physics · 2018
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 R n and Z among the pivot-monotonic transformations is proved.Faster formulas for the monotonic normalization of metrics are discussed.