Spatial Depth-Based Classification for Functional Data

TL;DR

This paper introduces the kernelized functional spatial depth (KFSD), a local and kernel-based extension of FSD, to improve functional data classification, especially in cases with subtle group differences or outliers.

Contribution

The paper proposes KFSD, a new local-oriented functional depth, and demonstrates its effectiveness in robust classification of functional data, outperforming existing methods.

Findings

KFSD improves classification accuracy in simulations.

KFSD performs well on real-world functional data.

KFSD is robust to outliers and subtle group differences.

Abstract

We enlarge the number of available functional depths by introducing the kernelized functional spatial depth (KFSD). KFSD is a local-oriented and kernel-based version of the recently proposed functional spatial depth (FSD) that may be useful for studying functional samples that require an analysis at a local level. In addition, we consider supervised functional classification problems, focusing on cases in which the differences between groups are not extremely clear-cut or the data may contain outlying curves. We perform classification by means of some available robust methods that involve the use of a given functional depth, including FSD and KFSD, among others. We use the functional \textit{k}-nearest neighbor classifier as a benchmark procedure. The results of a simulation study indicate that the KFSD-based classification approach leads to good results. Finally, we consider two real classification problems, obtaining results that are consistent with the findings observed with simulated curves.