Authors:
João Fernando Marar
1
and
Helder Coelho
2
Affiliations:
1
Adaptive Systems and Computational Intelligence Laboratory, Faculdade de Ciências, São Paulo State University, Brazil
;
2
Laboratory of Agent Modelling, Faculdade de Ciências, Lisbon University, Portugal
Keyword(s):
Artificial Neural Network, Function Approximation, Polynomial Powers of Sigmoid (PPS), Wavelets Functions,
PPS-Wavelet Neural Networks, Activation Functions, Feedforward Networks.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Biomedical Engineering
;
Biomedical Signal Processing
;
Computational Intelligence
;
Health Engineering and Technology Applications
;
Human-Computer Interaction
;
Methodologies and Methods
;
Neural Networks
;
Neurocomputing
;
Neurotechnology, Electronics and Informatics
;
Pattern Recognition
;
Physiological Computing Systems
;
Sensor Networks
;
Signal Processing
;
Soft Computing
;
Theory and Methods
Abstract:
Wavelet functions have been used as the activation function in feedforward neural networks. An abundance of R&D has been produced on wavelet neural network area. Some successful algorithms and applications in wavelet neural network have been developed and reported in the literature. However, most of the aforementioned reports impose many restrictions in the classical backpropagation algorithm, such as low dimensionality, tensor product of wavelets, parameters initialization, and, in general, the output is one dimensional, etc. In order to remove some of these restrictions, a family of polynomial wavelets generated from powers of sigmoid functions is presented. We described how a multidimensional wavelet neural networks based on these functions can be constructed, trained and applied in pattern recognition tasks. As an example of application for the method proposed, it is studied the exclusive-or (XOR) problem.