IDEAS home Printed from https://ideas.repec.org/a/spr/topjnl/v22y2014i3p815-840.html
   My bibliography  Save this article

Support vector machines maximizing geometric margins for multi-class classification

Author

Listed:
  • Keiji Tatsumi
  • Tetsuzo Tanino

Abstract

Machine learning is a very interesting and important branch of artificial intelligence. Among many learning models, the support vector machine is a popular model with high classification ability which can be trained by mathematical programming methods. Since the model was originally formulated for binary classification, various kinds of extensions have been investigated for multi-class classification. In this paper, we review some existing models, and introduce new models which we recently proposed. The models are derived from the viewpoint of multi-objective maximization of geometric margins for a discriminant function, and each model can be trained by solving a second-order cone programming problem. We show that discriminant functions with high generalization ability can be obtained by these models through some numerical experiments. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • Keiji Tatsumi & Tetsuzo Tanino, 2014. "Support vector machines maximizing geometric margins for multi-class classification," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 815-840, October.
    • Handle: RePEc:spr:topjnl:v:22:y:2014:i:3:p:815-840
    DOI: 10.1007/s11750-014-0338-8
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11750-014-0338-8
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11750-014-0338-8?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. Lee, Yoonkyung & Lin, Yi & Wahba, Grace, 2004. "Multicategory Support Vector Machines: Theory and Application to the Classification of Microarray Data and Satellite Radiance Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 67-81, January.
    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. Martín Barragán, Belén, 2016. "A Partial parametric path algorithm for multiclass classification," DES - Working Papers. Statistics and Econometrics. WS 22390, Universidad Carlos III de Madrid. Departamento de Estadística.

    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. Engin Tas & Ayca Hatice Atli, 2024. "Stock Price Ranking by Learning Pairwise Preferences," Computational Economics, Springer;Society for Computational Economics, vol. 63(2), pages 513-528, February.
    2. Hoai An Le Thi & Manh Cuong Nguyen, 2017. "DCA based algorithms for feature selection in multi-class support vector machine," Annals of Operations Research, Springer, vol. 249(1), pages 273-300, February.
    3. Pedro Duarte Silva, A., 2017. "Optimization approaches to Supervised Classification," European Journal of Operational Research, Elsevier, vol. 261(2), pages 772-788.
    4. Abramovich, Felix & Pensky, Marianna, 2019. "Classification with many classes: Challenges and pluses," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    5. Fang Yao & Yichao Wu & Jialin Zou, 2016. "Probability-enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-22, March.
    6. Guangrui Tang & Neng Fan, 2022. "A Survey of Solution Path Algorithms for Regression and Classification Models," Annals of Data Science, Springer, vol. 9(4), pages 749-789, August.
    7. Zhilan Lou & Jun Shao & Menggang Yu, 2018. "Optimal treatment assignment to maximize expected outcome with multiple treatments," Biometrics, The International Biometric Society, vol. 74(2), pages 506-516, June.
    8. Ozcan, Sercan & Suloglu, Metin & Sakar, C. Okan & Chatufale, Sushant, 2021. "Social media mining for ideation: Identification of sustainable solutions and opinions," Technovation, Elsevier, vol. 107(C).
    9. María Pérez-Ortiz & Silvia Jiménez-Fernández & Pedro A. Gutiérrez & Enrique Alexandre & César Hervás-Martínez & Sancho Salcedo-Sanz, 2016. "A Review of Classification Problems and Algorithms in Renewable Energy Applications," Energies, MDPI, vol. 9(8), pages 1-27, August.
    10. Yann Guermeur, 2014. "Comments on: Support Vector Machines Maximizing Geometric Margins for Multi-class Classification," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 844-851, October.
    11. Yang, Yi & Guo, Yuxuan & Chang, Xiangyu, 2021. "Angle-based cost-sensitive multicategory classification," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    12. Yoonkyung Lee, 2014. "Comments on: Support vector machines maximizing geometric margins for multi-class classification," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 852-855, October.
    13. Crystal T. Nguyen & Daniel J. Luckett & Anna R. Kahkoska & Grace E. Shearrer & Donna Spruijt‐Metz & Jaimie N. Davis & Michael R. Kosorok, 2020. "Estimating individualized treatment regimes from crossover designs," Biometrics, The International Biometric Society, vol. 76(3), pages 778-788, September.
    14. Maximilian Alber & Julian Zimmert & Urun Dogan & Marius Kloft, 2017. "Distributed optimization of multi-class SVMs," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-18, June.
    15. Gardner-Lubbe, Sugnet, 2016. "A triplot for multiclass classification visualisation," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 20-32.
    16. Fu, Sheng & Zhang, Sanguo & Liu, Yufeng, 2018. "Adaptively weighted large-margin angle-based classifiers," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 282-299.
    17. van den Burg, G.J.J. & Groenen, P.J.F., 2014. "GenSVM: A Generalized Multiclass Support Vector Machine," Econometric Institute Research Papers EI 2014-33, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    18. Sarra Houidi & Dominique Fourer & François Auger & Houda Ben Attia Sethom & Laurence Miègeville, 2021. "Comparative Evaluation of Non-Intrusive Load Monitoring Methods Using Relevant Features and Transfer Learning," Energies, MDPI, vol. 14(9), pages 1-28, May.
    19. Park, Beomjin & Park, Changyi, 2021. "Kernel variable selection for multicategory support vector machines," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    20. Liu, Yufeng & Helen Zhang, Hao & Park, Cheolwoo & Ahn, Jeongyoun, 2007. "Support vector machines with adaptive Lq penalty," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6380-6394, August.

    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:topjnl:v:22:y:2014:i:3:p:815-840. 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.