title: Ultrahigh-Dimensional Multiclass Linear Discriminant Analysis by Pairwise Sure Independence Screening.
abstract: This paper is concerned with the problem of feature screening for multi-class linear discriminant analysis under ultrahigh dimensional setting. We allow the number of classes to be relatively large. As a result, the total number of relevant features is larger than usual. This makes the related classification problem much more challenging than the conventional one, where the number of classes is small (very often two). To solve the problem, we propose a novel pairwise sure independence screening method for linear discriminant analysis with an ultrahigh dimensional predictor. The proposed procedure is directly applicable to the situation with many classes. We further prove that the proposed method is screening consistent. Simulation studies are conducted to assess the finite sample performance of the new procedure. We also demonstrate the proposed methodology via an empirical analysis of a real life example on handwritten Chinese character recognition.
authors.affiliation: Assistant Professor, School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, 100081.
authors.forename: Rui
authors.initials: R
authors.lastname: Pan
authors.affiliation: Professor, Guanghua School of Management, Peking University, Beijing, 100871, P.R. China.
authors.forename: Hansheng
authors.initials: H
authors.lastname: Wang
authors.affiliation: Professor, Department of Statistics and The Methodology Center, The Pennsylvania State University, University Park, PA 16802-2111.
authors.forename: Runze
authors.initials: R
authors.lastname: Li
keywords: Multi-class Linear Discriminant Analysis; Pairwise Sure Independence Screening; Strong Screening Consistency; Sure Independence Screening