### ASA 127th Meeting M.I.T. 1994 June 6-10

## 3aPP21. Radial basis function neural network for modeling auditory space.

**Rick L. Jenison
****
**
*Dept. of Psychol., Univ. of Wisconsin, Madison, WI 53706
*

*
*
**Kate Fissell
**

**
**
*Univ. of Wisconsin, Madison, WI 53706
*

*
*
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.]