Continuum centroid classifier for functional data

TL;DR

The paper introduces the continuum centroid classifier (CCC), a novel method for binary classification of functional data that leverages projections and a hybrid supervised approach, achieving asymptotic zero misclassification in some cases.

Contribution

It proposes a new CCC method that bridges regression and classification, controlling supervision to improve functional data classification.

Findings

CCC achieves asymptotic zero misclassification in some cases

The algorithm provides a consistent empirical version of CCC

Simulation and real data demonstrate CCC's effectiveness

Abstract

Aiming at the binary classification of functional data, we propose the continuum centroid classifier (CCC) built upon projections of functional data onto one specific direction. This direction is obtained via bridging the regression and classification. Controlling the extent of supervision, our technique is neither unsupervised nor fully supervised. Thanks to the intrinsic infinite dimension of functional data, one of two subtypes of CCC enjoys the (asymptotic) zero misclassification rate. Our proposal includes an effective algorithm that yields a consistent empirical counterpart of CCC. Simulation studies demonstrate the performance of CCC in different scenarios. Finally, we apply CCC to two real examples.