A new self-organizing neural network using geometric algebra

Abstract

This paper presents a new self-organizing type RBF neural network and introduces the geometric algebra framework in the neurocomputing field. Real valued neural nets for function approximation require feature enhancement, dilation and rotation operations and are limited by the Euclidean metric. The authors believe that more general and flexible neural networks should be designed in order to capture important geometric characteristics of the manifolds. This is an important goal overlooked ever since. Geometric algebra is a system which allows the design of neural networks in a coordinate-free frame work to process patterns between layers using different dimensions and desired metric. The potential of such nets working in a Clifford algebra C(V/sub p,q/) is shown by a simple application of frame coordination in robotics.