High-Dimensional Approximation using an Associative Memory Network

Bridgett, N.A., Brown, M., Harris, C.J. and Mills, D.J. (1994) High-Dimensional Approximation using an Associative Memory Network. Control'94.

Abstract

Various approaches exist to the problem of high-dimensional approximation (e.g. MARS, CART, ASMOD, ABBMOD) in an attempt to alleviate the curse of dimensionality - where the complexity or number of parameters required to construct an accurate model of a function in a Euclidean space increases exponentially with the dimension of the input space. The aim of this paper is to extract the salient features of these approaches and to provide a general framework for the development of an algorithm suitable for approximating the high-dimensional functions found in modelling and control problems (automatic generation of a fuzzy rule base). The points considered in the paper include: selecting the basis functions, model construction, the learning algorithm to optimise the linear coefficients in the approximation and the criteria for model structure evaluation. The approach selected is based on the ASMOD algorithm of Kavli, and results are presented based on a simple study of a time-series difference equation which are compared with results generated using an alternative approach (the MARS algorithm of Friedman).

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