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Cubic approximation neural network for multivariate functions

✍ Scribed by Doron Stein; Arie Feuer

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 374 KB
Volume: 11
Category: Article
ISSN: 0893-6080
DOI: 10.1016/s0893-6080(97)00150-0

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✦ Synopsis

This paper introduces a novel neural network architecture-cubic approximation neural network (CANN), capable of local approximation of multivariate functions. It is particularly simple in concept and in structure. Its simplicity enables a quantitative evaluation of its approximation capabilities, namely, for a desired error bound the size of the needed network can be calculated. In addition, if a training session is used, a thorough analysis of the learning process performance is performed. The trade-off between the rate of learning and the steady-state performance is clearly demonstrated. On the other hand, this approach suffers from the problem common to all local approximation networks-the number of neurons grows exponentially with the dimension of the input vector.

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