Improvement of wavelet neural network hybrid systems performance by optimisation of two types of learning algorithms

Two algorithms of hybrid, wavelet neural network system (WNS) structures, designed for specific application are presented. They describe the procedure of optimizing the wavelet transform (WT) scale parameter a in initial WNS layer. The type of learning algorithms depends on the features of wavelet basic function (WBF) used in WT signal decomposition. First algorithm, designed for Morlet WBF, which is expressed by analytical, differentiable formula, is based on modified error back propagation, used for multi-layer perceptron learning. Parameters of WNS with two remaining, tested WBFs - Db4 and Bior 2.4 were optimized according to the second proposed algorithm, which applies a predefined dyadic grid of scale a, and entropy analysis of Mallat multilevel decomposition, to choose the optimal decomposition level. The learning performance, characterized by speed and convergence of learning process, was verified in the field, specific for neural network applications. The base of non-stationary heart rate variability (HRV) signals, obtained from patients with coronary arm diseases of different level, divided into learning and verifying set was used. This type of signals was chosen, because the application of preliminary time-frequency analysis methods, especially the wavelet transform described in this paper, seems to be very good way for extraction the most important features, crucial for a given classification problem, included in HRV signal.