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Massive Data Classification via Unconstrained Support Vector Machines

Author

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  • O. L. Mangasarian

    (University of Wisconsin)

  • M. E. Thompson

    (University of Wisconsin)

Abstract

A highly accurate algorithm, based on support vector machines formulated as linear programs (Refs. 1–2), is proposed here as a completely unconstrained minimization problem (Ref. 3). Combined with a chunking procedure (Ref. 4), this approach, which requires nothing more complex than a linear equation solver, leads to a simple and accurate method for classifying million-point datasets. Because a 1-norm support vector machine underlies the proposed approach, the method suppresses input space features as well. A state-of-the-art linear programming package (CPLEX, Ref. 5) fails to solve problems handled by the proposed algorithm.

Suggested Citation

  • O. L. Mangasarian & M. E. Thompson, 2006. "Massive Data Classification via Unconstrained Support Vector Machines," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 315-325, December.
    • Handle: RePEc:spr:joptap:v:131:y:2006:i:3:d:10.1007_s10957-006-9157-x
    DOI: 10.1007/s10957-006-9157-x
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    References listed on IDEAS

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    1. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    2. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
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    Cited by:

    1. C. J. Lin & S. Lucidi & L. Palagi & A. Risi & M. Sciandrone, 2009. "Decomposition Algorithm Model for Singly Linearly-Constrained Problems Subject to Lower and Upper Bounds," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 107-126, April.
    2. Pedro Duarte Silva, A., 2017. "Optimization approaches to Supervised Classification," European Journal of Operational Research, Elsevier, vol. 261(2), pages 772-788.
    3. Carrizosa, Emilio & Nogales-Gómez, Amaya & Romero Morales, Dolores, 2017. "Clustering categories in support vector machines," Omega, Elsevier, vol. 66(PA), pages 28-37.
    4. Emilio Carrizosa & Belen Martin-Barragan & Dolores Romero Morales, 2010. "Binarized Support Vector Machines," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 154-167, February.

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