Operator-valued Kernels for Learning from Functional Response Data

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.

in Journal of Machine Learning Research (JMLR), 2016

References in corpus (5)

• A New Approach to Collaborative Filtering: Operator Estimation with Spectral Regularization
• Support vector machine for functional data classification
• Learning from Distributions via Support Measure Machines
• Operator-valued Kernels for Learning from Functional Response Data
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