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The Nonpolynomiality of the Number of Similarities for Random Training Sets

Published: 17 October 2024 Publication History

Abstract

Abstract

In this paper an additional argument is provided in favor of the probabilistic approach to knowledge extraction using the similarity operation (the VKF method) through the nonpolynomiality of the number of all candidates. More specifically, two results about such nonpolynomiality are proved for random training sets generated by Bernoulli trials. In the case of dense lattice, it is proved that the probability of appearance of a large sublattice that is isomorphic to Boolean algebra in the lattice of candidates tends to unity as the size of the set increases. For a lattice of medium density, a slightly modified Sakurai’s argument about the nonpolynomiality of the mean number of candidates is reproduced.

References

[1]
Feller W. An Introduction to Probability Theory and Its Applications 1968 New York Wiley
[2]
Finn V. K. and Anshakov O. M. JSM Method of Automatic Generation of Hypotheses. Logical and Epistemological Foundations 2009 Moscow URSS
[3]
Taro S. On formal concepts of random formal contexts Inf. Sci. 2021 578 615-620
[4]
Vinogradov D. V. Algebraic machine learning: Emphasis on efficiency Autom. Remote Control 2022 83 831-846

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        Published In

        cover image Pattern Recognition and Image Analysis
        Pattern Recognition and Image Analysis  Volume 34, Issue 3
        Sep 2024
        513 pages

        Publisher

        Springer-Verlag

        Berlin, Heidelberg

        Publication History

        Published: 17 October 2024
        Accepted: 12 February 2024
        Revision received: 24 January 2024
        Received: 18 December 2023

        Author Tags

        1. similarity
        2. Bernoulli trials
        3. lattice of candidates
        4. Boolean algebra

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