IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v17y2002i2d10.1007_s001800200106.html
   My bibliography  Save this article

Comparison between various regression depth methods and the support vector machine to approximate the minimum number of misclassifications

Author

Listed:
  • Andreas Christmann

    (University of Dortmund)

  • Paul Fischer

    (University of Dortmund)

  • Thorsten Joachims

    (Institute for Autonomous Intelligent Systems)

Abstract

Summary The minimum number of misclassifications achievable with affine hyperplanes on a given set of labeled points is a key quantity in both statistics and computational learning theory. However, determining this quantity exactly is NP-hard, c.f. Höffgen, Simon and van Horn (1995). Hence, there is a need to find reasonable approximation procedures. This paper introduces two new approaches to approximating the minimum number of misclassifications achievable with affine hyperplanes. Both approaches are modifications of the regression depth method proposed by Rousseeuw and Hubert (1999) for linear regression models. Our algorithms are compared to the existing regression depth algorithm (c.f. Christmann and Rousseeuw, 1999) for various data sets. We also used a support vector machine approach, as proposed by Vapnik (1998), as a reference method.

Suggested Citation

  • Andreas Christmann & Paul Fischer & Thorsten Joachims, 2002. "Comparison between various regression depth methods and the support vector machine to approximate the minimum number of misclassifications," Computational Statistics, Springer, vol. 17(2), pages 273-287, July.
  • Handle: RePEc:spr:compst:v:17:y:2002:i:2:d:10.1007_s001800200106
    DOI: 10.1007/s001800200106
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s001800200106
    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/s001800200106?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.

    Citations

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


    Cited by:

    1. Pavlo Mozharovskyi & Karl Mosler & Tatjana Lange, 2015. "Classifying real-world data with the $${ DD}\alpha $$ D D α -procedure," 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. 9(3), pages 287-314, September.
    2. Tatjana Lange & Karl Mosler & Pavlo Mozharovskyi, 2014. "Fast nonparametric classification based on data depth," Statistical Papers, Springer, vol. 55(1), pages 49-69, February.
    3. Christmann, Andreas, 2004. "On a strategy to develop robust and simple tariffs from motor vehicle insurance data," Technical Reports 2004,16, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Nedret Billor & Asheber Abebe & Asuman Turkmen & Sai Nudurupati, 2008. "Classification Based on Depth Transvariations," Journal of Classification, Springer;The Classification Society, vol. 25(2), pages 249-260, November.
    5. Christmann, Andreas & Steinwart, Ingo, 2003. "On robustness properties of convex risk minimization methods for pattern recognition," Technical Reports 2003,15, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    6. Christmann, Andreas, 2004. "Regression depth and support vector machine," Technical Reports 2004,54, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    7. Rousseeuw, Peter J. & Christmann, Andreas, 2003. "Robustness against separation and outliers in logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 43(3), pages 315-332, July.
    8. Dyckerhoff, Rainer & Mozharovskyi, Pavlo & Nagy, Stanislav, 2021. "Approximate computation of projection depths," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    9. Christmann, Andreas & Steinwart, Ingo & Hubert, Mia, 2007. "Robust learning from bites for data mining," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 347-361, September.
    10. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2017. "Multivariate and functional classification using depth and distance," 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. 11(3), pages 445-466, September.

    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:compst:v:17:y:2002:i:2:d:10.1007_s001800200106. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.