A reproducing kernel Hilbert space framework for functional data classification

TL;DR

This paper introduces a novel RKHS-based framework for functional data classification that projects infinite-dimensional data onto a single direction, enabling effective use of DWD classifiers with theoretical guarantees and practical advantages.

Contribution

It proposes a new RKHS projection method for functional data classification, providing non-asymptotic error bounds and demonstrating superior performance over existing methods.

Findings

The classifier achieves favorable prediction accuracy in simulations.

The method effectively handles scalar covariates in classification.

Theoretical error bounds support the classifier's reliability.

Abstract

We encounter a bottleneck when we try to borrow the strength of classical classifiers to classify functional data. The major issue is that functional data are intrinsically infinite dimensional, thus classical classifiers cannot be applied directly or have poor performance due to the curse of dimensionality. To address this concern, we propose to project functional data onto one specific direction, and then a distance-weighted discrimination DWD classifier is built upon the projection score. The projection direction is identified through minimizing an empirical risk function that contains the particular loss function in a DWD classifier, over a reproducing kernel Hilbert space. Hence our proposed classifier can avoid overfitting and enjoy appealing properties of DWD classifiers. This framework is further extended to accommodate functional data classification problems where scalar covariates are involved. In contrast to previous work, we establish a non-asymptotic estimation error bound on the relative misclassification rate. In finite sample case, we demonstrate that the proposed classifiers compare favorably with some commonly used functional classifiers in terms of prediction accuracy through simulation studies and a real-world application.