A Probabilistic Algorithm for Calculating Similarities


In this paper, we describe a new probabilistic algorithm for calculating hypotheses as the results of similarities between training examples for a machine learning problem based on a binary similarity operation. Unlike previously proposed probabilistic algorithms, the order of accounting for training examples is fixed for all hypotheses. This algorithm is useful for implementation using a GPGPU. The main result of this paper is the independence of the order of the appearance of training examples of the probabilities of each similarity in the sample.

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

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA


  1. 1

    DSM-metod avtomaticheskogo porozhdeniya gipotez: Logicheskie i epistemologicheskie osnovaniya (JSM Method for Automatic Hypothesis Generation: Logical and Epistemological Foundations), Finn, V.K. and Anshakov, O.M., Eds., Moscow: Editorial-URSS, 2009.

  2. 2

    Ganter, B. and Wille, R., Formal Concept Analysis, Berlin: Springer-Verlag, 1999.

  3. 3

    Vinogradov, D.V., The rate of convergence to the limit of the probability of encountering an accidental similarity in the presence of counter examples, Autom. Doc. Math. Linguist., 2018, vol. 52, no. 1, pp. 35–37.

  4. 4

    Vinogradov, D.V., Accidental formal concepts in the presence of counterexamples, Proceedings of International Workshop on Formal Concepts Analysis for Knowledge Discovery (FCA4KD 2017):CEUR Workshop Proceedings, 2017, vol. 1921, pp. 104–112.

  5. 5

    Vinogradov, D.V., Random generation of hypotheses in the JSM method using simple Markov chains, Autom. Doc. Math. Linguist., 2012, vol. 46, no. 5, pp. 221–228.

  6. 6

    Vinogradov, D.V., Machine learning based on similarity operation, Commun. Comput. Inf. Sci., 2018, vol. 934, pp. 46–59.

  7. 7

    Vinogradov, D.V., The reliability of analogy-based prediction, Autom. Doc. Math. Linguist., 2017, vol. 51, no. 4, pp. 191–195.

  8. 8

    Vapnik, V.N. and Chervonenkis, A.Ya., Teoriya raspoznavaniya obrazov (statisticheskie problemy obucheniya) (Pattern Recognition Theory (Statistical Learning Problems)), Moscow: Nauka, 1974.

  9. 9

    Davey, B.A. and Priestley, H.A., Introduction to Lattices and Order, Cambridge: Cambridge University Press, 2002, 2nd ed.

  10. 10

    Vinogradov, D.V., On object representation by bit strings for the VKF-method, Autom. Doc. Math. Linguist., 2018, vol. 52, no. 3, pp. 113–116.

Download references


The author thanks his colleagues from the Informatics and Management FRC, Russian Academy of Sciences for constructive criticism and useful comments.


This work was partially supported by the Russian Foundation for Basic Research, project no. 18-29-03063mk.

Author information

Correspondence to D. V. Vinogradov.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

Translated by A. Ivanov

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Vinogradov, D.V. A Probabilistic Algorithm for Calculating Similarities. Autom. Doc. Math. Linguist. 53, 234–236 (2019) doi:10.3103/S0005105519050042

Download citation


  • similarity
  • probabilistic algorithm
  • counter-example