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