Approximation of multivariate functions using ridge polynomial networks

A novel class of higher-order feedforward neural networks, called the ridge polynomial network (RPN), is formulated. The networks are shown to uniformly approximate any continuous function of a compact set in multidimensional input space with any degree of accuracy. These networks have an efficient and regulator architecture as compared to ordinary higher-order feedforward networks. The RPNs use a special form of ridge polynomials. It is shown that any multivariate polynomial can be represented in terms of this ridge polynomial, and realized by an RPN. The RPN is a generalization of the pi-sigma network which provides a natural mechanism for incremental network growth. Simulation results are provided to show the approximation capability of an incremental learning algorithm of the RPNs