# MULTIDIMENSIONAL POLYNOMIAL POWERS OF SIGMOID (PPS) WAVELET NEURAL NETWORKS

### João Fernando Marar, Helder Coelho

#### 2008

#### 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.

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#### Paper Citation

#### in Harvard Style

Fernando Marar J. and Coelho H. (2008). **MULTIDIMENSIONAL POLYNOMIAL POWERS OF SIGMOID (PPS) WAVELET NEURAL NETWORKS** . In *Proceedings of the First International Conference on Bio-inspired Systems and Signal Processing - Volume 2: BIOSIGNALS, (BIOSTEC 2008)* ISBN 978-989-8111-18-0, pages 261-268. DOI: 10.5220/0001067302610268

#### in Bibtex Style

@conference{biosignals08,

author={João Fernando Marar and Helder Coelho},

title={MULTIDIMENSIONAL POLYNOMIAL POWERS OF SIGMOID (PPS) WAVELET NEURAL NETWORKS},

booktitle={Proceedings of the First International Conference on Bio-inspired Systems and Signal Processing - Volume 2: BIOSIGNALS, (BIOSTEC 2008)},

year={2008},

pages={261-268},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001067302610268},

isbn={978-989-8111-18-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the First International Conference on Bio-inspired Systems and Signal Processing - Volume 2: BIOSIGNALS, (BIOSTEC 2008)

TI - MULTIDIMENSIONAL POLYNOMIAL POWERS OF SIGMOID (PPS) WAVELET NEURAL NETWORKS

SN - 978-989-8111-18-0

AU - Fernando Marar J.

AU - Coelho H.

PY - 2008

SP - 261

EP - 268

DO - 10.5220/0001067302610268