Functional Regularized Least Squares Classi cation with Operator-valued Kernels

TL;DR

This paper investigates operator-valued kernels in functional data analysis, extending the Regularized Least Squares Classification algorithm to handle multiple functions per observation, demonstrating improved performance in sound recognition tasks.

Contribution

It introduces an operator-valued kernel feature space perspective and extends RLSC to multi-function data, enhancing classification performance.

Findings

Proposed method outperforms classical RLSC in sound recognition

Extended RLSC to handle multiple functions per observation

Provides new insights into operator-valued kernel feature spaces

Abstract

Although operator-valued kernels have recently received increasing interest in various machine learning and functional data analysis problems such as multi-task learning or functional regression, little attention has been paid to the understanding of their associated feature spaces. In this paper, we explore the potential of adopting an operator-valued kernel feature space perspective for the analysis of functional data. We then extend the Regularized Least Squares Classification (RLSC) algorithm to cover situations where there are multiple functions per observation. Experiments on a sound recognition problem show that the proposed method outperforms the classical RLSC algorithm.