Wave‐net: a multiresolution, hierarchical neural network with localized learning

TLDR

Wave‑Net is a neural network that uses orthonormal wavelet basis functions, enabling localized, multiresolution learning and explicit global and local error‑bound estimation. The article develops the mathematical framework for Wave‑Nets and discusses their practical implementation. It presents two application examples: predicting a chaotic time‑series of population dynamics and classifying experimental data for process fault diagnosis. Computational complexity analysis shows Wave‑Nets train and adapt at least an order of magnitude faster than other networks.

Abstract

Abstract A Wave‐Net is an artificial neural network with one hidden layer of nodes, whose basis functions are drawn from a family of orthonormal wavelets. The good localization characteristics of the basis functions, both in the input and frequency domains, allow hierarchical, multiresolution learning of input‐output maps from experimental data. Furthermore, Wave‐Nets allow explicit estimation for global and local prediction error‐bounds, and thus lend themselves to a rigorous and explicit design of the network. This article presents the mathematical framework for the development of Wave‐Nets and discusses the various aspects of their practical implementation. Computational complexity arguments prove that the training and adaptation efficiency of Wave‐Nets is at least an order of magnitude better than other networks. In addition, it presents two examples on the application of Wave‐Nets; (a) the prediction of a chaotic time‐series, representing population dynamics, and (b) the classification of experimental data for process fault diagnosis.