Flexible High-Dimensional Discrimination

• Activity Number: 15
• Type: Topic Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Xingye Qiao*+ and Lingsong Zhang
• Companies: Binghamton University and Purdue University
• Keywords: Classification ; High-dimensional, low-sample size ; Fisher consistency

Abstract

Discrimination is an important problem in statistical machine learning research with great potential in many applications. There are many challenges, especially for high-dimensional data. One challenge is the unbalanced sample size issue. The class with a greater sample size overly influences the classifier and pushes the classification boundary to the minority class. Another challenge is the loss of generalization ability issue, partially due to data-piling under the high-dimensional, low-sample size setting, addressed in Marron et al. (2007). Although there has been development for a discrimination method that overcomes one of these challenges, for example Support Vector Machine (SVM) and Distance Weighted Discrimination (DWD), existing methods have difficulty in dealing with both issues at the same time. We propose a hybrid discrimination method that combines the advantages of both SVM and DWD. The proposed method, Flexible High-dimensional Discrimination (FHD), improves DWD by making it flexible to unbalanced sample size, and improves SVM by alleviating the high-dimensional data-piling, which consequentially improves the generalization ability.