Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

On L1-Norm Multiclass Support Vector Machines: Methodology and Theory

Lifeng Wang and Xiaotong Shen
Journal of the American Statistical Association
Vol. 102, No. 478 (Jun., 2007), pp. 583-594
Stable URL: http://www.jstor.org/stable/27639888
Page Count: 12
  • Download ($14.00)
  • Cite this Item
On L1-Norm Multiclass Support Vector Machines: Methodology and Theory
Preview not available

Abstract

Binary support vector machines (SVMs) have been proven to deliver high performance. In multiclass classification, however, issues remain with respect to variable selection. One challenging issue is classification and variable selection in the presence of variables in the magnitude of thousands, greatly exceeding the size of training sample. This often occurs in genomics classification. To meet the challenge, this article proposes a novel multiclass support vector machine, which performs classification and variable selection simultaneously through an L1-norm penalized sparse representation. The proposed methodology, together with the developed regularization solution path, permits variable selection in such a situation. For the proposed methodology, a statistical learning theory is developed to quantify the generalization error in an attempt to gain insight into the basic structure of sparse learning, permitting the number of variables to greatly exceed the sample size. The operating characteristics of the methodology are examined through both simulated and benchmark data and are compared against some competitors in terms of accuracy of prediction. The numerical results suggest that the proposed methodology is highly competitive.

Page Thumbnails

  • Thumbnail: Page 
583
    583
  • Thumbnail: Page 
584
    584
  • Thumbnail: Page 
585
    585
  • Thumbnail: Page 
586
    586
  • Thumbnail: Page 
587
    587
  • Thumbnail: Page 
588
    588
  • Thumbnail: Page 
589
    589
  • Thumbnail: Page 
590
    590
  • Thumbnail: Page 
591
    591
  • Thumbnail: Page 
592
    592
  • Thumbnail: Page 
593
    593
  • Thumbnail: Page 
594
    594