A New Type of a Wavelet Neural Network

Abstract

Wavelet transformation uses a special basis widely known for its unique properties, the most important of which are its compactness and multiresolution (wavelet functions are produced from the mother wavelet by transition and dilation). Wavelet neural networks (WNN) use wavelet functions to decompose the approximated function. However, for a standard wavelet basis with fixed transition and dilation coefficients, the decomposition may be not optimal. If no inverse transformation is needed, the values of transition and dilation coefficients may be determined during network training, and the windows corresponding to various wavelet functions may overlap. In this study, we suggest a new type of a WNN—Adaptive Window WNN (AWWNN), designed primarily for signal processing, in which window positions and wavelet levels are determined with a special iterative procedure. Two modifications of this new type of WNN are tested against linear model and multi-layer perceptron on Mackey-Glass benchmark problem.