Multiclass Distance-Weighted Discrimination for High-Dimensional, Low-Sample Size Data

• Activity Number: 544
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2014 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Hanwen Huang*+ and Xingye Qiao and Lingsong Zhang
• Companies: University of Georgia and SUNY Binghampton University and Purdue Univeristy
• Keywords: Multiclass classi cation ; Fisher consistency; ; Variable selection

Abstract

Multiclass distance weighted discrimination (MDWD) is a powerful tool for classification. In this article, we focus on analyzing High-Dimensional, Low-Sample Size (HDLSS) data. First, we propose three different approaches to achieve sparsity, including the so-called L_{1,1} penalty, L_{1,2} penalty and L_{1,\infty} penalty. We compare the properties of the three properties and stress that the latter two can achieve real variable selection. Second, we propose to use the coefficient matrix estimated by MDWD to conduct data projection and visualization for the HDLSS data. Third, we conduct a series of comprehensive theoretical studies with regards to the multiclass classification problem in the HDLSS setting. In particular, a relatively new type of asymptotics under the `n fixed, d goes to infinity' setting is studied which is useful in our study. Last, simulations and real data application shows the usefulness of our sparse MDWD methods and verify the HDLSS theoretical results.