Ridge polynomial networks

This paper presents a polynomial connectionist network called ridge polynomial network (RPN) that can uniformly approximate any continuous function on a compact set in multidimensional input space R (d), with arbitrary degree of accuracy. This network provides a more efficient and regular architecture compared to ordinary higher-order feedforward networks while maintaining their fast learning property. The ridge polynomial network is a generalization of the pi-sigma network and uses a special form of ridge polynomials. It is shown that any multivariate polynomial can be represented in this form, and realized by an RPN. Approximation capability of the RPN's is shown by this representation theorem and the Weierstrass polynomial approximation theorem. The RPN provides a natural mechanism for incremental network growth. Simulation results on a surface fitting problem, the classification of high-dimensional data and the realization of a multivariate polynomial function are given to highlight the capability of the network. In particular, a constructive learning algorithm developed for the network is shown to yield smooth generalization and steady learning.