Optimal Linear Discriminant Analysis for High-Dimensional Functional Data

Kaijie Xue, Jin Yang and Fang Yao

Journal of the American Statistical Association, 2024, vol. 119, issue 546, 1055-1064

Abstract: 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. Supplementary materials for this article are available online.

Date: 2024
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://hdl.handle.net/10.1080/01621459.2022.2164288 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlasa:v:119:y:2024:i:546:p:1055-1064

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/UASA20

DOI: 10.1080/01621459.2022.2164288

Access Statistics for this article

Journal of the American Statistical Association is currently edited by Xuming He, Jun Liu, Joseph Ibrahim and Alyson Wilson

More articles in Journal of the American Statistical Association from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().