Principal Weighted Support Vector Machines for Sufficient Dimension Reduction in Binary Classification

• Activity Number: 570 - New Frontiers of Functional Data Analysis
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2018 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Hao Helen Zhang*
• Companies: University of Arizona
• Keywords: kernel machines; weighted Support vector machines; sufficient dimension reduction; reproducing kernel Hilbert space ; nonparametric; binary classification

Abstract

Sufficient dimension reduction is popular for reducing data dimensionality without stringent model assumptions. However, most existing methods may work poorly for binary classification. For example, sliced inverse regression (Li, 1991) can estimate at most one direction if the response is binary. In this paper we propose principal weighted support vector machines, a unified framework for linear and nonlinear sufficient dimension reduction in binary classification. Its asymptotic properties are studied, and an efficient computing algorithm is proposed. Numerical examples demonstrate its performance in binary classification.