Wavelet Neural Networks: A Practical Guide

Abstract

Abstract-Wavelet networks (WNs) are a new class of networks which have been used with great success in a wide range of application. However a general accepted framework for applying WNs is missing from the literature. In this study, we present a complete statistical model identification framework in order to apply WNs in various applications. The following subjects were thorough examined: the structure of a WN, training methods, initialization algorithms, variable significance and variable selection algorithms, model selection methods and finally methods to construct confidence and prediction intervals. In addition the complexity of each algorithm is discussed. Our proposed framework was tested in two simulated cases, in one chaotic time series described by the Mackey-Glass equation and in three real datasets described by daily temperatures in Berlin, daily wind speeds in New York and breast cancer classification. Our results have shown that the proposed algorithms produce stable and robust results indicating that our proposed framework can be applied in various applications.

Comparing various artificial neural network types for water temperature prediction in rivers

“…In a number of studies it was shown that various data pre-processing techniques (Wu et al, 2009), especially the wavelet transform (Alexandridis and Zapranis, 2013), may improve the performance of hydrological modelling (Wang and Ding, 2003;Nourani et al, 2009;Tiwari and Chatterjee, 2010;Adamowski and Chan, 2011;Kisi and Cimen, 2011;Maheswaran and Khosa, 2014;Adamowski and Prokoph, 2014). The wavelet transform is an effective decomposition method that provides a way of analyzing signal in both time and frequency domains, contrary to the conventional Fourier transforms that do provide time-frequency analysis for the variables with stationary signals.…”

Modeling induction-based steam distillation system by using nonlinear auto-regressive with exogenous input (NLARX) structure

“…The temperature of the steam must be balanced, not too low or high. This is because, when the temperature is too high, it will burn the plant material or affect the quality and rate of output yield [4]. The purpose of this research is to model the steam distillation system by using system identification tool in MATLAB R2013a software.…”

“…This wavelet network is commonly used in signal processing and time series analysis [4]. Wavelet network is normally in the form of three layers network.…”

Empirical modelling and prediction of neuronal dynamics

“…We also consider the identity function of each state variable. As proposed in (Alexandridis & Zapranis, 2011;Fisco-Compte, 2020), it might be useful to reduce the prediction error. This is equivalent to approximating f (x) − L(x), where L(x) is a linear function of the state input vector, instead of f (x) in equation ( 1), by the neural network.…”