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Mimicking Learning for 1-NN Classifiers

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Computational Science – ICCS 2021 (ICCS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12744))

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Abstract

We consider the problem of mimicking the behavior of the nearest neighbor algorithm with an unknown distance measure. Our goal is, in particular, to design and update a learning set so that two NN algorithms with various distance functions \(\rho _{p}\) and \(\rho _{q}\), \(0<p,q<\infty ,\) classify in the same way, and to approximate the behavior of one classifier by the other. The autism disorder-related motivation of the problem is presented.

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Notes

  1. 1.

    Hence, if \(L^{*}\) is small, the performance of the NN algorithm can be acceptable, [2, Ch. 2.1 and 5.2].

  2. 2.

    See https://github.com/Bahrd/Voronoi for the Python scripts.

  3. 3.

    Note that, due to randomness of the patterns \(\left\{ X_{n}\right\} ,\) the grid points are not equidistant.

  4. 4.

    The k-NN algorithm can however be used to model a known classifier (a ‘teacher’).

  5. 5.

    This relatively new scientific discipline aims at developing and examining theoretical and computational models that could serve as a basis for new therapies and/or medicines.

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Acknowledgments

Authors want to thank the Reviewers for their comments and suggestions.

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Authors and Affiliations

  1. Wrocław University of Science and Technology, 50-370, Wrocław, Poland

    Przemysław Śliwiński & Paweł Wachel

  2. University of Arizona, Tucson, AZ, 85721, USA

    Jerzy W. Rozenblit

Authors
  1. Przemysław Śliwiński
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  2. Paweł Wachel
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  3. Jerzy W. Rozenblit
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Corresponding author

Correspondence to Przemysław Śliwiński .

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Editors and Affiliations

  1. AGH University of Science and Technology, Krakow, Poland

    Maciej Paszynski

  2. Ludwig-Maximilians-Universität München, Munich, Germany

    Dieter Kranzlmüller

  3. University of Amsterdam, Amsterdam, The Netherlands

    Valeria V. Krzhizhanovskaya

  4. University of Tennessee at Knoxville, Knoxville, TN, USA

    Jack J. Dongarra

  5. University of Amsterdam, Amsterdam, The Netherlands

    Peter M.A. Sloot

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Śliwiński, P., Wachel, P., Rozenblit, J.W. (2021). Mimicking Learning for 1-NN Classifiers. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12744. Springer, Cham. https://doi.org/10.1007/978-3-030-77967-2_7

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  • DOI: https://doi.org/10.1007/978-3-030-77967-2_7

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  • Online ISBN: 978-3-030-77967-2

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