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A novel piecewise linear classifier based on polyhedral conic and max–min separabilities

Author

Listed:
  • Adil Bagirov
  • Julien Ugon
  • Dean Webb
  • Gurkan Ozturk
  • Refail Kasimbeyli

Abstract

In this paper, an algorithm for finding piecewise linear boundaries between pattern classes is developed. This algorithm consists of two main stages. In the first stage, a polyhedral conic set is used to identify data points which lie inside their classes, and in the second stage we exclude those points to compute a piecewise linear boundary using the remaining data points. Piecewise linear boundaries are computed incrementally starting with one hyperplane. Such an approach allows one to significantly reduce the computational effort in many large data sets. Results of numerical experiments are reported. These results demonstrate that the new algorithm consistently produces a good test set accuracy on most data sets comparing with a number of other mainstream classifiers. Copyright Sociedad de Estadística e Investigación Operativa 2013

Suggested Citation

  • Adil Bagirov & Julien Ugon & Dean Webb & Gurkan Ozturk & Refail Kasimbeyli, 2013. "A novel piecewise linear classifier based on polyhedral conic and max–min separabilities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 3-24, April.
    • Handle: RePEc:spr:topjnl:v:21:y:2013:i:1:p:3-24
    DOI: 10.1007/s11750-011-0241-5
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    References listed on IDEAS

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    1. A. Astorino & M. Gaudioso, 2002. "Polyhedral Separability Through Successive LP," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 265-293, February.
    2. Youngtae Park & Jack Sklansky, 1989. "Automated design of multiple-class piecewise linear classifiers," Journal of Classification, Springer;The Classification Society, vol. 6(1), pages 195-222, December.
    3. A. M. Bagirov & B. Karasözen & M. Sezer, 2008. "Discrete Gradient Method: Derivative-Free Method for Nonsmooth Optimization," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 317-334, May.
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    Cited by:

    1. A. R. Doagooei, 2015. "Minimum Type Functions, Plus-Cogauges, and Applications," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 551-564, February.
    2. Víctor Blanco & Alberto Japón & Justo Puerto, 2020. "Optimal arrangements of hyperplanes for SVM-based multiclass classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(1), pages 175-199, March.
    3. Annabella Astorino & Antonio Fuduli, 2015. "Support Vector Machine Polyhedral Separability in Semisupervised Learning," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 1039-1050, March.
    4. A. Sheykhi & A. R. Doagooei, 2017. "Radiant Separation Theorems and Minimum-Type Subdifferentials of Calm Functions," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 693-711, September.

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