The asymptotic properties of a -classifier for multiclass recognition problems with non-elliptic distribution of data

Authors

  • O. A. Galkin Taras Shevchenko National University of Kiev

DOI:

https://doi.org/10.15407/dopovidi2016.06.025

Keywords:

Bayes rule, Σ-classifier, asymptotic convergence

Abstract

The asymptotic properties of a Σ-classifier that does not require a priori information about the distribution or shape of a dividing curve are studied. A mathematical apparatus is built to solve multiclass recognition problems with a non-elliptic distribution of data on the basis of the majority voting method. The procedure is studied to determine the shapes of dividing curves of a Σ-classifier by the geometric structure of data that are the basis of the Σ-scheme. The conditions, under which the Σ-classifier is asymptotically equivalent to the Bayes rule, are defined.

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References

Galkin О. А. Bull. of Taras Shevchenko National University of Kiev. Ser. Phys. & Math., 2015, No 3: 60–65 (in Ukrainian).

Lange T., Mosler K, Mozharovskyi P. Statist. Papers, 2014, 55: 53–67.

Cuesta-Albertos J. A., Nieto-Reyes A. Computational Statistics & Data Analysis, 2008, 52: 4980–4987.

Li J., Zuo R. Y. Statistical Sci., 2004, 19: 687–694.

Zuo Y. J. The Annals of Statistics, 2003, 31: 1463–1484.

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Published

03.11.2024

How to Cite

Galkin, O. A. (2024). The asymptotic properties of a -classifier for multiclass recognition problems with non-elliptic distribution of data. Reports of the National Academy of Sciences of Ukraine, (6), 25–31. https://doi.org/10.15407/dopovidi2016.06.025

Issue

No. 6 (2016): Reports of the National Academy of Sciences of Ukraine

Section

Information Science and Cybernetics

License

Copyright (c) 2024 Reports of the National Academy of Sciences of Ukraine

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