Multivariable Approximation by Convolutional Kernel Networks

Abstrakt

Computational units induced by convolutional kernels together with biologically inspired perceptrons belong to the most widespread types of units used in neurocomputing. Radial convolutional kernels with varying widths form RBF (radial-basis-function) networks and these kernels with fixed widths are used in the SVM (support vector machine) algorithm. We investigate suitability of various convolutional kernel units for function approximation. We show that properties of Fourier transforms of convolutional kernels determine whether sets of input-output functions of networks with kernel units are large enough to be universal approximators. We compare these properties with conditions guaranteeing positive semidefinitness of convolutional kernels.