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Teoriya Veroyatnostei i ee Primeneniya, 2020, Volume 65, Issue 3, Pages 479–497
DOI: https://doi.org/10.4213/tvp5267 (Mi tvp5267) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On the complexity and dimension of continuous finite-dimensional maps

B. S. Darkhovskyab

a Institute for Systems Analysis of Russian Academy of Sciences
b Russian University of Transport
Full-text PDF (476 kB) Citations (6)
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DOI: https://doi.org/10.4213/tvp5267
Abstract: We introduce the concept of $\varepsilon$-complexity of an individual continuous finite-dimensional map. This concept is in good accord with the principle of A. N. Kolmogorov's idea of measuring complexity of objects. It is shown that the $\varepsilon$-complexity of an “almost all” Hölder map can be effectively described. This description can be used as a basis for a model-free technique for segmentation and classification of data of arbitrary nature. A new definition of the dimension of the graph of a map is also proposed.
Keywords: $\varepsilon$-complexity, continuous maps, model-free classification and segmentation of data.
Funding agency Grant number
Russian Foundation for Basic Research 17-29-02115
20-07-00221
Received: 06.11.2018
Revised: 25.12.2019
Accepted: 20.01.2020
English version:
Theory of Probability and its Applications, 2020, Volume 65, Issue 3, Pages 375–387
DOI: https://doi.org/10.1137/S0040585X97T990010
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: B. S. Darkhovsky, “On the complexity and dimension of continuous finite-dimensional maps”, Teor. Veroyatnost. i Primenen., 65:3 (2020), 479–497; Theory Probab. Appl., 65:3 (2020), 375–387
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp/v65/i3/p479
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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    References:41
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