RIDGE POLYNOMIAL NETWORKS

This paper presents a polynomial connectionist network called ridge po lynomial network (RPN) that can uniformly approximate any continuous f unction on a compact set in multidimensional input space R(d), with ar bitrary degree of accuracy, This network provides a more efficient and regular architecture compared to ordinary higher-order feedforward ne tworks while maintaining their fast learning property. The ridge polyn omial network is a generalization of the pi-sigma network and uses a s pecial form of ridge polynomials, It is shown that any multivariate po lynomial can be represented in this form, and realized by an RPN, Appr oximation capability of the RPN's is shown by this;representation theo rem and the Weierstrass polynomial approximation theorem, The RPN prov ides a natural mechanism for incremental network growth, Simulation re sults on a surface fitting problem, the classification of high-dimensi onal data and the realization of a multivariate polynomial function ar e given to highlight the capability of the network, In particular, a c onstructive learning algorithm developed for the network is shown to y ield smooth generalization and steady learning,