A centroid classifier for functional/longitudinal data

Abstract

The problem of classifying functional data has raised great research interests. When functional data are fully observed random trajectories, many classifiers have been recently proposed. However in practice, functional data may be observed discretely based on a regular or irregular design with the measurements that are contaminated by noise. In this paper, we define a new classifier to classify functional/longitudinal data based on the original discrete observations and under a general weighing scheme. We then study the theoretical properties of the proposed centroid classifier, and establish that the proposed classification rule is consistently estimated by its empirical version. The empirical performance is illustrated through a simulation study and two real data sets.

Keywords:

• Classification
• componentwise centroid
• functional/longitudinal data
• smoothing
• weighing scheme

2010 Mathematics Subject Classification:

• 62H30

Acknowledgments

We thank the Associate Editor and the referee for providing constructive comments. Moreover, the support and resources from the centre for High Performance Computing at the Shahid Beheshti University of Iran are gratefully acknowledged.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported in part by the Iranian National Science Foundation (INSF) [grant number 97015261].