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Nearest Convex Hull Classification Based on Linear Programming

  • MATHEMATICAL THEORY OF PATTERN RECOGNITION
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Abstract

Machine learning methods for automatic classification problems using computational geometry are considered. Classes are defined by convex hulls of sets of points in a multidimensional feature space. The classification algorithms based on the evaluation of the proximity of a test point to the convex hulls of classes are examined. A new method for proximity evaluation based on linear programming is proposed. The corresponding nearest convex hull classifier is described. The results of experimental studies on real problems of medical diagnostics are presented. The comparison of the effectiveness of the proposed classifier with the classifiers of other types has shown a sufficiently high efficiency of the proposed method for proximity evaluation based on linear programming.

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Funding

This study was supported in part by the Russian Foundation for Basic Research, project nos. 19-29-01009 and 18-29-02036.

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Authors and Affiliations

  1. Saint Petersburg Electrotechnical University “LETI”, 197376, St. Petersburg, Russia

    Anatoly Nemirko

  2. University of Alabama, 23487, Tuscaloosa, AL, U.S.A.

    José H. Dulá

Authors
  1. Anatoly Nemirko
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  2. José H. Dulá
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Corresponding authors

Correspondence to Anatoly Nemirko or José H. Dulá.

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The authors declare that they have no conflicts of interest. This article does not contain any studies involving animals or human participants performed by any of the authors.

Additional information

Anatoly Pavlovich Nemirko. Graduated from St. Petersburg Electrotechnical University LETI in 1967. Since 1986, has worked as a professor at the Department of Bioengineering Systems at the same university. Received doctoral degree in 1986 and professor degree in 1988. Scientific interests: pattern recognition, processing and analysis of biomedical signals, intelligent biomedical systems. Author of more than 300 scientific publications including 90 papers and five monographs. Board member of the International Association of Pattern Recognition and member of the editorial board of the journal Pattern Recognition and Image Analysis.

José H. Dulá. B.S.E. and Ph.D. from the University of Michigan in 1980 and 1986 with a M.Sc. from Stanford University in 1981. He is currently Professor of Operations Management at the University of Alabama having been previously at Virginia Commonwealth University until 2018. He works primarily in operations research topics, more specifically in optimization, computational geometry, data envelopment analysis and, more recently, machine learning. He is an author in Operations Research, Mathematical Programming, INFORMS Journal on Computing, European Journal of Operational Research, among others. He is associate editor for the International Transactions of OR and Journal of Productivity Analysis.

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Nemirko, A., Dulá, J.H. Nearest Convex Hull Classification Based on Linear Programming. Pattern Recognit. Image Anal. 31, 205–211 (2021). https://doi.org/10.1134/S1054661821020139

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