Operatorvalued 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 kernelbased learning are extended to include the estimation of functionvalued functions. In this setting, the representer theorem is restated, a set of rigorously defined infinitedimensional operatorvalued 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2015
 arXiv:
 arXiv:1510.08231
 Bibcode:
 2015arXiv151008231K
 Keywords:

 Computer Science  Machine Learning;
 Statistics  Machine Learning
 EPrint:
 in Journal of Machine Learning Research (JMLR), 2016