Skip to main content
SpringerLink
Log in

On Some Factorizations of Semi-Metric Cones and Quality Estimates of Heuristic Metrics in Data Analysis Problems

  • COMPUTER SCIENCE
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

An approach is proposed to consider heuristic metrics introduced and used in data analysis problems. In the approach, the entire information on pairwise distances expressed by numerical values is reduced to information on a metric belonging as a point of a semi-metric cone to corresponding subcones, which are elements of factor sets for proposed relations of kernel equivalences for mappings into formal index families.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. Yu. I. Zhuravlev, in Problems in Cybernetics (Nauka, Moscow, 1978), Vol. 33, pp. 5–68 [in Russian].

    Google Scholar 

  2. K. V. Vorontsov, Mathematical Methods for Instance-Based Learning: A Course of Lectures (Mosk. Fiz.-Tekh. Inst., Moscow, 2006) [in Russian].

    Google Scholar 

  3. M. M. Deza and M. Laurent, Geometry of Cuts and Metrics (Springer-Verlag, Berlin, 1997).

    Book  Google Scholar 

  4. A. I. Mal’tsev, Algebraic Systems (Nauka, Moscow, 1970) [in Russian].

    MATH  Google Scholar 

  5. A. V. Arutyunov, Lectures on Convex and Set-Valued Analysis (Fizmatlit, Moscow, 2014) [in Russian].

    Google Scholar 

Download references

Funding

This work was performed at the Dorodnicyn Computing Center of the Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences in the course of the research “Mathematical Foundations of Smart Big Data Analysis” conducted at the Center of Big Data Storage and Analysis Technology of Lomonosov Moscow State University and was supported by the Russian Foundation for Basic Research, project no. 18-07-00741.

Author information

Authors and Affiliations

  1. Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, 119333, Moscow, Russia

    K. V. Rudakov

  2. Center of Big Data Storage and Analysis Technology, Lomonosov Moscow State University, 119192, Moscow, Russia

    K. V. Rudakov

Authors
  1. K. V. Rudakov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. V. Rudakov.

Additional information

Translated by I. Ruzanova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rudakov, K.V. On Some Factorizations of Semi-Metric Cones and Quality Estimates of Heuristic Metrics in Data Analysis Problems. Dokl. Math. 101, 257–258 (2020). https://doi.org/10.1134/S1064562420030230

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562420030230

Keywords:

Search

Navigation