Ultrahigh-Dimensional Multiclass Linear Discriminant Analysis by Pairwise Sure Independence Screening

• 成果类型: Article
• 署名作者: Pan, Rui; Wang, Hansheng; Li, Runze
• 署名单位: Central University of Finance & Economics; Peking University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.998760
• 发表日期: 2016
• 页码: 169-179
• 关键词: Classification

摘要

This article is concerned with the problem of feature screening for multiclass 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.