IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v131y2006i3d10.1007_s10957-006-9157-x.html
   My bibliography  Save this article

Massive Data Classification via Unconstrained Support Vector Machines

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-006-9157-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-006-9157-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Pedro Duarte Silva, A., 2017. "Optimization approaches to Supervised Classification," European Journal of Operational Research, Elsevier, vol. 261(2), pages 772-788.
    4. Carrizosa, Emilio & Nogales-Gómez, Amaya & Romero Morales, Dolores, 2017. "Clustering categories in support vector machines," Omega, Elsevier, vol. 66(PA), pages 28-37.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sankaran, Jayaram K., 1995. "Column generation applied to linear programs in course registration," European Journal of Operational Research, Elsevier, vol. 87(2), pages 328-342, December.
    2. François Clautiaux & Cláudio Alves & José Valério de Carvalho & Jürgen Rietz, 2011. "New Stabilization Procedures for the Cutting Stock Problem," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 530-545, November.
    3. Omid Shahvari & Rasaratnam Logendran & Madjid Tavana, 2022. "An efficient model-based branch-and-price algorithm for unrelated-parallel machine batching and scheduling problems," Journal of Scheduling, Springer, vol. 25(5), pages 589-621, October.
    4. Ibrahim Muter & Tevfik Aytekin, 2017. "Incorporating Aggregate Diversity in Recommender Systems Using Scalable Optimization Approaches," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 405-421, August.
    5. Barry C. Smith & Ellis L. Johnson, 2006. "Robust Airline Fleet Assignment: Imposing Station Purity Using Station Decomposition," Transportation Science, INFORMS, vol. 40(4), pages 497-516, November.
    6. Fırat, M. & Briskorn, D. & Laugier, A., 2016. "A Branch-and-Price algorithm for stable workforce assignments with hierarchical skills," European Journal of Operational Research, Elsevier, vol. 251(2), pages 676-685.
    7. Klose, Andreas & Gortz, Simon, 2007. "A branch-and-price algorithm for the capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1109-1125, June.
    8. Figielska, Ewa, 2014. "A heuristic for scheduling in a two-stage hybrid flowshop with renewable resources shared among the stages," European Journal of Operational Research, Elsevier, vol. 236(2), pages 433-444.
    9. Timo Gschwind & Stefan Irnich, 2014. "Dual Inequalities for Stabilized Column Generation Revisited," Working Papers 1407, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz, revised 23 Jul 2014.
    10. Víctor M. Albornoz & Gabriel E. Zamora, 2021. "Decomposition-based heuristic for the zoning and crop planning problem with adjacency constraints," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 248-265, April.
    11. Peng, Zixuan & Shan, Wenxuan & Zhu, Xiaoning & Yu, Bin, 2022. "Many-to-one stable matching for taxi-sharing service with selfish players," Transportation Research Part A: Policy and Practice, Elsevier, vol. 160(C), pages 255-279.
    12. Syam Menon & Rakesh Gupta, 2008. "Optimal Broadcast Scheduling in Packet Radio Networks via Branch and Price," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 391-399, August.
    13. Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2016. "Bin packing and cutting stock problems: Mathematical models and exact algorithms," European Journal of Operational Research, Elsevier, vol. 255(1), pages 1-20.
    14. Daniel Adelman & George L. Nemhauser, 1999. "Price-Directed Control of Remnant Inventory Systems," Operations Research, INFORMS, vol. 47(6), pages 889-898, December.
    15. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    16. Tolou Esfandeh & Rajan Batta & Changhyun Kwon, 2018. "Time-Dependent Hazardous-Materials Network Design Problem," Transportation Science, INFORMS, vol. 52(2), pages 454-473, March.
    17. Uçar, Ezgi & İlker Birbil, Ş. & Muter, İbrahim, 2017. "Managing disruptions in the multi-depot vehicle scheduling problem," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 249-269.
    18. Andrew Allman & Qi Zhang, 2021. "Branch-and-price for a class of nonconvex mixed-integer nonlinear programs," Journal of Global Optimization, Springer, vol. 81(4), pages 861-880, December.
    19. Leão, Aline A.S. & Santos, Maristela O. & Hoto, Robinson & Arenales, Marcos N., 2011. "The constrained compartmentalized knapsack problem: mathematical models and solution methods," European Journal of Operational Research, Elsevier, vol. 212(3), pages 455-463, August.
    20. Zhu, Wenbin & Huang, Weili & Lim, Andrew, 2012. "A prototype column generation strategy for the multiple container loading problem," European Journal of Operational Research, Elsevier, vol. 223(1), pages 27-39.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:131:y:2006:i:3:d:10.1007_s10957-006-9157-x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.