Dynamic Ridge Polynomial Higher Order Neural Network

Abstract

This chapter proposes a novel Dynamic Ridge Polynomial Higher Order Neural Network (DRPHONN). The architecture of the new DRPHONN incorporates recurrent links into the structure of the ordinary Ridge Polynomial Higher Order Neural Network (RPHONN) (Shin & Ghosh, 1995). RPHONN is a type of feedforward Higher Order Neural Network (HONN) (Giles & Maxwell, 1987) which implements a static mapping of the input vectors. In order to model dynamical functions of the brain, it is essential to utilize a system that is capable of storing internal states and can implement complex dynamic system. Neural networks with recurrent connections are dynamical systems with temporal state representations. The dynamic structure approach has been successfully used for solving varieties of problems, such as time series forecasting (Zhang & Chan, 2000; Steil, 2006), approximating a dynamical system (Kimura & Nakano, 2000), forecasting a stream flow (Chang et al, 2004), and system control (Reyes et al, 2000). Motivated by the ability of recurrent dynamic systems in real world applications, the proposed DRPHONN architecture is presented in this chapter.