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J. Sib. Fed. Univ. Math. Phys., 2018, Volume 11, Issue 3, Pages 331–341 (Mi jsfu680)  

This article is cited in 2 scientific papers (total in 2 papers)

From similarity to distance: axiom set,monotonic transformations and metric determinacy

Sergej V. Znamenskij

Ailamazyan Program Systems Institute of RAS, Peter the First Street 4, Veskovo village, Pereslavl area,Yaroslavl region, 152021, Russia

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 $\mathbb{R}^n$ and $\mathbb{Z}$ among the pivot-monotonic transformations is proved. Faster formulas for the monotonic normalization of metrics are discussed.

Keywords: metric space, similarity axioms, similarity normalization, metric determinacy, longest common subsequence.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation RFMEFI60716X0153
This work was performed under financial support from the Government, represented by the Ministry of Education and Science of the Russian Federation (Project ID RFMEFI60716X0153).


DOI: https://doi.org/10.17516/1997-1397-2018-11-3-331-341

Full text: PDF file (379 kB)
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Bibliographic databases:

UDC: 004.412
Received: 18.11.2017
Received in revised form: 22.12.2017
Accepted: 20.02.2018
Language:

Citation: Sergej V. Znamenskij, “From similarity to distance: axiom set,monotonic transformations and metric determinacy”, J. Sib. Fed. Univ. Math. Phys., 11:3 (2018), 331–341

Citation in format AMSBIB
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\paper From similarity to distance: axiom set,monotonic transformations and metric determinacy
\jour J. Sib. Fed. Univ. Math. Phys.
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\vol 11
\issue 3
\pages 331--341
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Znamenskij, “Stable assessment of the quality of similarity algorithms of character strings and their normalizations”, Programmnye sistemy: teoriya i prilozheniya, 9:4 (2018), 561–578  mathnet  crossref
    2. S. V. Znamenskii, “Ustoichivaya otsenka kachestva algoritmov skhodstva simvolnykh strok i ikh normalizatsii”, Programmnye sistemy: teoriya i prilozheniya, 9:4 (2018), 579–596  mathnet  crossref
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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