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On a Robust Approach to Search for Cluster Centers

Authors
  • Shibzukhov, Z. M.1, 2
  • 1 Institute of Mathematics and Computer Science, Moscow Pedagogical State University, Moscow, 119991, Russia , Moscow (Russia)
  • 2 Moscow Institute of Physics and Technology, Dolgoprudnyi, Moscow oblast, 141701, Russia , Dolgoprudnyi (Russia)
Type
Published Article
Journal
Automation and Remote Control
Publisher
Pleiades Publishing
Publication Date
Oct 01, 2021
Volume
82
Issue
10
Pages
1742–1751
Identifiers
DOI: 10.1134/S0005117921100118
Source
Springer Nature
Keywords
Disciplines
  • Article
License
Yellow

Abstract

Abstract We propose a new approach to the construction of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k $$\end{document}-means clustering algorithms in which the Mahalanobis distance is used instead of the Euclidean distance. The approach is based on minimizing differentiable estimates of the mean insensitive to outliers. Illustrative examples convincingly show that the proposed algorithm is highly likely to be robust with respect to a large amount of outliers in the data.

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