TY - CHAP

T1 - Analysis and improvement of function approximation capabilities of pi-sigma higher order neural networks

AU - Murata, Junichi

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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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U2 - 10.4018/978-1-61520-711-4.ch010

DO - 10.4018/978-1-61520-711-4.ch010

M3 - Chapter

AN - SCOPUS:84898579329

SN - 9781615207114

SP - 239

EP - 254

BT - Artificial Higher Order Neural Networks for Computer Science and Engineering: Trends for Emerging Applications

PB - IGI Global

ER -