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Analysis and Improvement of Function Approximation Capabilities of Pi-Sigma Higher Order Neural Networks

Analysis and Improvement of Function Approximation Capabilities of Pi-Sigma Higher Order Neural Networks

Junichi Murata
Copyright: © 2010 |Pages: 16
ISBN13: 9781615207114|ISBN10: 1615207112|ISBN13 Softcover: 9781616922511|EISBN13: 9781615207121
DOI: 10.4018/978-1-61520-711-4.ch010
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MLA

Murata, Junichi. "Analysis and Improvement of Function Approximation Capabilities of Pi-Sigma Higher Order Neural Networks." Artificial Higher Order Neural Networks for Computer Science and Engineering: Trends for Emerging Applications, edited by Ming Zhang, IGI Global, 2010, pp. 239-254. https://doi.org/10.4018/978-1-61520-711-4.ch010

APA

Murata, J. (2010). Analysis and Improvement of Function Approximation Capabilities of Pi-Sigma Higher Order Neural Networks. In M. Zhang (Ed.), Artificial Higher Order Neural Networks for Computer Science and Engineering: Trends for Emerging Applications (pp. 239-254). IGI Global. https://doi.org/10.4018/978-1-61520-711-4.ch010

Chicago

Murata, Junichi. "Analysis and Improvement of Function Approximation Capabilities of Pi-Sigma Higher Order Neural Networks." In Artificial Higher Order Neural Networks for Computer Science and Engineering: Trends for Emerging Applications, edited by Ming Zhang, 239-254. Hershey, PA: IGI Global, 2010. https://doi.org/10.4018/978-1-61520-711-4.ch010

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Abstract

A Pi-Sigma higher order neural network (Pi-Sigma HONN) is a type of higher order neural network, where, as its name implies, weighted sums of inputs are calculated first and then the sums are multiplied by each other to produce higher order terms that constitute the network outputs. This type of higher order neural networks have good function approximation capabilities. In this chapter, the structural feature of Pi-Sigma HONNs is discussed in contrast to other types of neural networks. The reason for their good function approximation capabilities is given based on pseudo-theoretical analysis together with empirical illustrations. Then, based on the analysis, an improved version of Pi-Sigma HONNs is proposed which has yet better function approximation capabilities.

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