On L1-Norm Multiclass Support Vector Machines: Classification of High-Dimension, Low Sample Size Data

• Activity Number: 187
• Type: Topic Contributed
• Date/Time: Monday, July 30, 2007 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Lifeng Wang*+ and Xiaotong Shen
• Companies: University of Pennsylvania and The University of Minnesota
• Keywords: High-dimension and low sample size ; Margin classification ; Regularization ; Sparsity ; Variable selection

Abstract

Binary support vector machines (SVM) have proven to deliver high performance. In multiclass classification, issues remain with respect to variable selection. A 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. We propose a novel multiclass SVM, which, together with a developed regularization solution path, perform classification and variable selection simultaneously through an L1-norm penalized sparse representation. 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 numerical results suggest that the proposed methodology is highly competitive.