Radial basis function neural network for modeling auditory space

Abstract

A neural network model is presented for approximating free-field-to-eardrum transfer functions (HRTFs) from a set of measured HRTFs. Learning an input–output mapping from examples is something that neural networks have been designed to perform and can be thought of as forming an approximation of a multivariate function. The mapping of input spherical coordinates (azimuth and elevation) to output HRTFs can be accomplished using an approximating function composed of a fixed number of basis functions and parameters that are estimated through a process of optimization. Radially symmetric functions, known as radial basis functions (RBFs), can serve as the set of nonorthogonal bases with the Gaussian often the basis function of choice. An important consideration in setting up the RBF architecture is choosing a sufficient number of basis functions as well as choosing the placement of the basis functions in order to adequately cover the two-dimensional input space. A gradient descent algorithm is presented that automatically learns the optimal placement and size of the RBFs such that the predicted HRTF mean-squared error is minimized. Other basis functions that are more appropriate for working on the sphere, such as the von Mises–Fisher function, will also be discussed. [Work supported by ONR and Wisconsin Alumni Research Foundation.]