ABSTRACT
We provide a rigorous account of high-dimensional kernels
(HDK), and illuminate their theoretical and practical advantages
in nonlinear regression of multivariate signals. Our emphasis
is on signal processing applications, supported by deep insight
into the existence of higher-dimensional feature spaces, including
complex, quaternion, and vector-valued reproducing kernel Hilbert
spaces. Next, these existence conditions are used to elucidate the
ability of kernel regression algorithms to extract rich relationships
from available data. Practical examples of the advantages of the
HDK paradigm include multimodal wind prediction, body sensor
trajectory tracking, and nonlinear function approximation.
