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A New Topology for Artificial Higher Order Neural Networks: Polynomial Kernel Networks

A New Topology for Artificial Higher Order Neural Networks: Polynomial Kernel Networks
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Author(s): Zhao Lu (Tuskegee University, USA), Leang-san Shieh (University of Houston, USA) and Guanrong Chen (City University of Hong Kong, China)
Copyright: 2009
Pages: 12
Source title: Artificial Higher Order Neural Networks for Economics and Business
Source Author(s)/Editor(s): Ming Zhang (Christopher Newport University, USA)
DOI: 10.4018/978-1-59904-897-0.ch019

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Abstract

Aiming to develop a systematic approach for optimizing the structure of artificial higher order neural networks (HONN) for system modeling and function approximation, a new HONN topology, namely polynomial kernel networks, is proposed in this chapter. Structurally, the polynomial kernel network can be viewed as a three-layer feedforward neural network with a special polynomial activation function for the nodes in the hidden layer. The new network is equivalent to a HONN; however, due to the underlying connections with polynomial kernel support vector machines, the weights and the structure of the network can be determined simultaneously using structural risk minimization. The advantage of the topology of the polynomial kernel network and the use of a support vector kernel expansion paves the way to represent nonlinear functions or systems, and underpins some advanced analysis of the network performance. In this chapter, from the perspective of network complexity, both quadratic programming and linear programming based training of the polynomial kernel network are investigated.

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