Fisher Discrimination Matrix and Dimension Reduction

• Activity Number: 324
• Type: Contributed
• Date/Time: Tuesday, August 2, 2016 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Debmalya Nandy* and Weixin Yao and Bruce George Lindsay and Francesca George Chiaromonte
• Companies: Penn State University and University of California at Riverside and Penn State University and Penn State University
• Keywords: Dimension Reduction ; Information Matrix

Abstract

A new data analysis tool called Fisher Discrimination Matrix (FDM) is developed to find the best directions that separate two densities via a simple eigen-analysis. We discuss several applications of FDM such as multiple linear discriminants, projection pursuit, independent component analysis, and graphical models. Based on FDM, we further introduce a new tool called Covariate Information Matrix (CIM). The CIM naturally provides a new method for Sufficient Dimension Reduction (SDR). This novel method identifies the minimal sufficient projection of the covariate vector in a regression problem, and also provides a natural rank ordering of its coordinates by their importance in terms of the covariate information. Simulation studies and real data applications demonstrate the effectiveness of the new SDR method compared to some existing techniques. B.G. Lindsay passed away due to an illness in May 2015. We lost a dear friend, a generous mentor and a brilliant colleague whose insight and rigor were instrumental to the development of this methodology, and whose contribution we would like to honor.