A Spherical Basis Function Neural Network for Modeling Auditory Space

This paper describes a neural network for approximation problems on the sphere. The von Mises basis function is introduced, whose activation depends on polar rather than Cartesian input coordinates. The architecture of the von Mises Basis Function (VMBF) neural network is presented along with the corresponding gradient-descent learning rules. The VMBF neural network is used to solve a particular spherical problem of approximating acoustic parameters used to model perceptual auditory space. This model ultimately serves as a signal processing engine to synthesize a virtual auditory environment under headphone listening conditions. Advantages of the VMBF over standard planar Radial Basis Functions (RBFs) are discussed.

[1]  D. Broomhead,et al.  Radial Basis Functions, Multi-Variable Functional Interpolation and Adaptive Networks , 1988 .

[2]  Nicholas I. Fisher,et al.  Statistical Analysis of Spherical Data. , 1987 .

[3]  K. J. Arnold.  On spherical probability distributions , 1941 .

[4]  D. M. Green,et al.  Directional sensitivity of sound-pressure levels in the human ear canal. , 1989, The Journal of the Acoustical Society of America.

[5]  F L Wightman,et al.  Headphone simulation of free-field listening. I: Stimulus synthesis. , 1989, The Journal of the Acoustical Society of America.

[6]  S. Carlile,et al.  Measuring the human head-related transfer functions: a novel method for the construction and calibration of a miniature "in-ear" recording system. , 1994, The Journal of the Acoustical Society of America.

[7]  F. Girosi,et al.  Networks for approximation and learning , 1990, Proc. IEEE.

[8]  James D. Keeler,et al.  Predicting the Future: Advantages of Semilocal Units , 1991, Neural Computation.

[9]  F. Wightman,et al.  A model of head-related transfer functions based on principal components analysis and minimum-phase reconstruction. , 1992, The Journal of the Acoustical Society of America.

[10]  G. Wahba.  Spline Interpolation and Smoothing on the Sphere , 1981 .

[11]  G. Wahba,et al.  Some New Mathematical Methods for Variational Objective Analysis Using Splines and Cross Validation , 1980 .

[12]  Barry D. Van Veen,et al.  Synthesis of 3D virtual auditory space via a spatial feature extraction and regularization model , 1993, Proceedings of IEEE Virtual Reality Annual International Symposium.

[13]  David S. Broomhead,et al.  Multivariable Functional Interpolation and Adaptive Networks , 1988, Complex Syst..

[14]  C. H. Chiang,et al.  Kinematics of Spherical Mechanisms , 1988 .

[15]  M. J. D. Powell,et al.  Radial basis functions for multivariable interpolation: a review , 1987 .

[16]  S. Cohn,et al.  Applications of Estimation Theory to Numerical Weather Prediction , 1981 .

[17]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[18]  K. Mardia.  Statistics of Directional Data , 1972 .