Optimizing Basis Function Selection in Constructive Wavelet Neural Networks and Its Applications

TL;DR

This paper presents a novel constructive wavelet neural network framework that optimizes basis function selection based on frequency analysis, enhancing accuracy and reducing computational costs across various signal processing applications.

Contribution

It introduces a frequency-based basis selection method and a constructive framework for wavelet neural networks, improving efficiency and applicability in nonlinear mapping tasks.

Findings

Significantly improves computational efficiency in wavelet neural networks.

Effectively estimates unknown static and time-varying mappings.

Demonstrates broad applicability through four diverse examples.

Abstract

Wavelet neural network (WNN), which learns an unknown nonlinear mapping from the data, has been widely used in signal processing, and time-series analysis. However, challenges in constructing accurate wavelet bases and high computational costs limit their application. This study introduces a constructive WNN that selects initial bases and trains functions by introducing new bases for predefined accuracy while reducing computational costs. For the first time, we analyze the frequency of unknown nonlinear functions and select appropriate initial wavelets based on their primary frequency components by estimating the energy of the spatial frequency component. This leads to a novel constructive framework consisting of a frequency estimator and a wavelet-basis increase mechanism to prioritize high-energy bases, significantly improving computational efficiency. The theoretical foundation defines the necessary time-frequency range for high-dimensional wavelets at a given accuracy. The framework's versatility is demonstrated through four examples: estimating unknown static mappings from offline data, combining two offline datasets, identifying time-varying mappings from time-series data, and capturing nonlinear dependencies in real time-series data. These examples showcase the framework's broad applicability and practicality. All the code will be released at https://github.com/dshuangdd/CWNN.