An optimal aggregation type classifier

TL;DR

This paper proposes a nonlinear aggregation classifier for functional data that combines multiple classifiers, ensuring consistency and asymptotic optimality, with simulation results demonstrating its effectiveness in high-dimensional and functional data contexts.

Contribution

Introduces a novel nonlinear aggregation rule for functional data classification that guarantees consistency and asymptotic optimality when combining arbitrary classifiers.

Findings

Aggregation rule is consistent if individual classifiers are consistent

Asymptotically performs as well as the best individual classifier

Simulation results show effectiveness for high-dimensional and functional data

Abstract

We introduce a nonlinear aggregation type classifier for functional data defined on a separable and complete metric space. The new rule is built up from a collection of $M$ arbitrary training classifiers. If the classifiers are consistent, then so is the aggregation rule. Moreover, asymptotically the aggregation rule behaves as well as the best of the $M$ classifiers. The results of a small si\-mu\-lation are reported both, for high dimensional and functional data.