Operator-valued Kernels for Learning from Functional Response Data

TL;DR

This paper introduces operator-valued kernels within reproducing kernel Hilbert space theory to enable supervised learning tasks involving functional data, such as speech and audio signals.

Contribution

It extends kernel-based learning to handle function-valued attributes and labels, providing a new framework for nonlinear functional data analysis.

Findings

Effective in speech and audio signal processing

Provides a rigorous theoretical foundation for functional data learning

Introduces a novel operator-valued kernel-based learning algorithm

Abstract

In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of reproducing kernel Hilbert space theory to learn from such functional data. Basic concepts and properties of kernel-based learning are extended to include the estimation of function-valued functions. In this setting, the representer theorem is restated, a set of rigorously defined infinite-dimensional operator-valued kernels that can be valuably applied when the data are functions is described, and a learning algorithm for nonlinear functional data analysis is introduced. The methodology is illustrated through speech and audio signal processing experiments.