Ultrahigh Dimensional Multi-Class Linear Discriminant Analysis by Pairwise Sure Independence Screening

36 Pages Posted: 9 Feb 2015

See all articles by Rui Pan

Rui Pan

Peking University

Hansheng Wang

Peking University - Guanghua School of Management

Runze Li

Pennsylvania State University

Date Written: February 8, 2015

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.

Keywords: Multi-class Linear Discriminant Analysis; Pairwise Sure Independence Screening; Sure Independence Screening; Strong Screening Consistency

JEL Classification: C35

Suggested Citation

Pan, Rui and Wang, Hansheng and Li, Runze, Ultrahigh Dimensional Multi-Class Linear Discriminant Analysis by Pairwise Sure Independence Screening (February 8, 2015). Available at SSRN: https://ssrn.com/abstract=2562126 or http://dx.doi.org/10.2139/ssrn.2562126

Rui Pan

Peking University ( email )

No. 38 Xueyuan Road
Haidian District
Beijing, Beijing 100871
China

Hansheng Wang (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

Runze Li

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

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