Stochastic models in artificial intelligence development

Oksana L. Kyrychenko; Igor V. Malyk; Sergey E. Ostapov

doi:10.17721/1812-5409.2021/2.7

Authors

Oksana L. Kyrychenko Yuriy Fedkovych Chernivtsi National University, 58012, Chernivtsi, Kotsiubynsky str, 2 https://orcid.org/0000-0003-0282-9958
Igor V. Malyk Yuriy Fedkovych Chernivtsi National University, 58012, Chernivtsi, Kotsiubynsky str, 2 https://orcid.org/0000-0002-1291-9167
Sergey E. Ostapov Yuriy Fedkovych Chernivtsi National University, 58012, Chernivtsi, Kotsiubynsky str, 2

DOI:

https://doi.org/10.17721/1812-5409.2021/2.7

Keywords:

stochastic random matrix, spectrum of a matrix, optimal number of clusters

Abstract

In this paper, we consider some properties of stochastic random matrices of large dimensions under conditions of independence of matrix elements or under conditions of independence of rows (columns). The main properties of stochastic random matrices spectrum are analyzed and the result of convergence to 0 is proved of almost all eigenvalues. Also, the application of these results to clustering problems and selection of the optimal number of clusters is considered. Note that the results obtained in this work are consistent with the Marchenko - Pastur theorem on the asymptotic distribution of eigenvalues of random matrices with independent elements. The results proved in this paper can be interpreted as a law of large numbers and will be used in the study of the asymptotic behavior of the maximum.

Pages of the article in the issue: 53 - 57

Language of the article: Ukrainian

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