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Nearest neighbors methods for support vector machines

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  • S. Camelo
  • M. González-Lima
  • A. Quiroz

Abstract

A key issue in the practical applicability of the support vector machine methodology is the identification of the support vectors in very large data sets, a problem to which a great deal of attention has been given in the literature. In the present article we propose methods based on sampling and nearest neighbors, that allow for an efficient implementation of an approximate solution to the classification problem and, at least in some problems, will help in identifying a significant fraction of the support vectors in large data sets at low cost. The performance of the proposed method is evaluated in different examples and some of its theoretical properties are discussed. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • S. Camelo & M. González-Lima & A. Quiroz, 2015. "Nearest neighbors methods for support vector machines," Annals of Operations Research, Springer, vol. 235(1), pages 85-101, December.
    • Handle: RePEc:spr:annopr:v:235:y:2015:i:1:p:85-101:10.1007/s10479-015-1956-8
    DOI: 10.1007/s10479-015-1956-8
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    References listed on IDEAS

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    1. Brito, M.R. & Quiroz, A.J. & Yukich, J.E., 2013. "Intrinsic dimension identification via graph-theoretic methods," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 263-277.
    2. Luca Zanni, 2006. "An Improved Gradient Projection-based Decomposition Technique for Support Vector Machines," Computational Management Science, Springer, vol. 3(2), pages 131-145, April.
    3. Brito, María R. & Quiroz, Adolfo J. & Yukich, J. E., 2002. "Graph-Theoretic Procedures for Dimension Identification," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 67-84, April.
    4. Brito, M. R. & Chávez, E. L. & Quiroz, A. J. & Yukich, J. E., 1997. "Connectivity of the mutual k-nearest-neighbor graph in clustering and outlier detection," Statistics & Probability Letters, Elsevier, vol. 35(1), pages 33-42, August.
    5. Asa Ben-Hur & Cheng Soon Ong & Sören Sonnenburg & Bernhard Schölkopf & Gunnar Rätsch, 2008. "Support Vector Machines and Kernels for Computational Biology," PLOS Computational Biology, Public Library of Science, vol. 4(10), pages 1-10, October.
    6. Lembke B., 1918. "√ a. p," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 111(1), pages 709-712, February.
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    Cited by:

    1. Roberto Bárcenas & Maria Gonzalez-Lima & Joaquin Ortega & Adolfo Quiroz, 2022. "On Subsampling Procedures for Support Vector Machines," Mathematics, MDPI, vol. 10(20), pages 1-27, October.
    2. Pablo Aparicio-Ruiz & Elena Barbadilla-Martín & José Guadix & Pablo Cortés, 2021. "KNN and adaptive comfort applied in decision making for HVAC systems," Annals of Operations Research, Springer, vol. 303(1), pages 217-231, August.
    3. Maria D. Gonzalez-Lima & Carenne C. Ludeña, 2022. "Using Locality-Sensitive Hashing for SVM Classification of Large Data Sets," Mathematics, MDPI, vol. 10(11), pages 1-21, May.

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