Multidimensional wavelet neural networks Based on polynomial powers of sigmoid

A framework to image verification


  • João Fernando Marar
  • Aron Bordin



Artificial neural network, Human face verification, mage processing, Pattern recognition, Polynomial powers of Sigmoid (PPS), Wavelets


Wavelet functions have been used as the activation function in feed forward 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 back propagation 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 examples of applications for the method proposed a framework for face verfication is presented.


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AVCI, E. (2007). An expert system based on wavelet neural network-adaptive norm entropy for scale invariant texture classification. Expert Systems with Applications, 32:919–926.

CHEN, H. and HEWIT, J. (2000). Application of wavelet transform and neural networks to recognition and classiffication of blemishes. Mechatronics, 10:699–711.

CHEN, Y., YANG, B., and DONG, J. (2006). Time series prediction using a local linear wavelet neural network. Neurocomputing, (69):449–465.

CHUI, C. (1992). An Introduction to Wavelets. Academic Press.

CYBENKO, G. (1989). Approximation by superposition of a sigmoidal function. Mathematics of Control, signals and Systems, 3:303–314.

DAUBECHIES, I. (1992). Ten lecture on wavelets. Society for Industrial and Applied Mathematics (SIAM).

DEPARTMENT, P. (2003). Psycological image collection at stirling university.

QUEIROZ, R. A. B. and MARAR, J. F. (2007). Algorítmos heurísticos para a seleção de neurônios em redes neurais polinomios potências de sigmoide (pps)-wavelet. TEMA Tend. Mat. Apl. Comput., 8(1):129–138.

FAN, J. and WANG, X. F. (2005). A wavelet view of small-world networks. IEEE Transactions on Circuits and Systems, pages 1–4.

FUNAHASHI, K. (1989). On the approximate realization of continuos mappings by neural networks. Neural Networks, (2):183–192.

GONZALEZ, R. C. and WOODS, R. E. (2002). Digital Image Processing. Prentice-Hall, Inc.

HECHT-NILSEN, R. (1987). Kolmogorov’s mapping neural networks existence theorem. In 1st IEEE Inter. Conf. on Neural Networks, volume 3, pages 11–14.

JIANG, X., MAHADEVAN1, S., and ADELI, H. (2007). Bayesian wavelet packet denoising for structural system identification. Struct. Control Health Monit., 14:333–356.

LIN, C. and FAN, K.-C. (2001). Triangle basead approuch to detection of human face. Pattern Recognition Society, pages 941–944.

MARAR, J. F. (1997). Polinomios Potências de Sigmoide (PPS): Uma nova Técnica para Aproximação de Funções, Construção de Wavenets e suas aplicações em Processamento de Imagens e Sinais. PhD thesis, Universidade Federal de Pernambuco - Departamento de Informática.

MARAR, J. F., COSTA, D., PINHEIRO, O., and FILHO, E. (2004). Adaptative techniques for the human faces detection. In 6th International Conference on Enterprise Information Systems, volume 2, pages 465–468.

MISRA, B. B., DASH, P. K., and PANDA, G. (2007). Pattern classification using local linear wavelet neural network. International Conference on Informa-tion and Communication Technology, pages 92–95.

OUSSAR, Y. and DREYFUS, G. (2000). Initialization by selection for wavelet neural traing. Neurocomputing, 34:131–143.

PATI, Y. and KRISHNAPRASAD, P. (1993). Analysis and synthesis of feedforward neural networks using discrete affine wavelet transformations. IEEE Transactions on Neural Networks, 4(1):73–85.

ZHANG, H. and PU, J. (2006). A novel self-adaptive control framework via wavelet neural netwok. In 6th World congress on intelligent control and automation, pages 2254–2258.

ZHANG, Q. and BENVENISTE, A. (1992). Wavelet networks. IEEE Transactions on Neural Networks, 3(6):889–898.

ZHANG, Z. and SAN, Y. (2004). Adaptive wavelet neural network for prediction of hourly nox and no2 concentrations. In Winter Simulation Conference, pages 1770–1778.



How to Cite

Marar, J. F., & Bordin, A. (2016). Multidimensional wavelet neural networks Based on polynomial powers of sigmoid: A framework to image verification. DAT Journal, 1(2), 106–123.