Optimal Linear Discriminant Analysis for High-Dimensional Functional Data

• 成果类型: Article
• 署名作者: Xue, Kaijie; Yang, Jin; Yao, Fang
• 署名单位: Nankai University; National Institutes of Health (NIH) - USA; NIH Eunice Kennedy Shriver National Institute of Child Health & Human Development (NICHD); Peking University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2164288
• 发表日期: 2024
• 页码: 1055-1064
• 关键词: Classification; regression; selection; CLASSIFIERS; models

摘要

Most of existing methods of functional data classification deal with one or a few processes. In this work we tackle classification of high-dimensional functional data, in which each observation is potentially associated with a large number of functional processes, p, which is comparable to or even much larger than the sample size n. The challenge arises from the complex inter-correlation structures among multiple functional processes, instead of a diagonal correlation for a single process. Since truncation is often needed for approximation in functional data, another difficulty stems from the fact that the discriminant set of the infinite-dimensional optimal classifier may be different from that of the truncated optimal classifier, when multiple (especially a large number of) processes are involved. We bridge the gap by proposing a penalized classifier that achieves both near-perfect classification that is unique to functional data, and discriminant set inclusion consistency in the sense that the classification-responsible functional predictors include those of the underlying optimal classifier. Simulation study and real data application are carried out to demonstrate its favorable performance. for this article are available online.