Neuralized Multi-Wavelet Decomposition for Time Series Classification and Forecasting

2026-09-24

AI Summary

This study addresses the limited representational capacity of existing time-series analysis methods caused by the decoupling of time-frequency structures. To overcome this, we propose the m-WCN framework, which introduces a core innovation by transforming the classical multiwavelet transform into trainable convolutional operators subject to orthogonality constraints for the first time. Leveraging deep convolutional networks, m-WCN achieves end-to-end joint time-frequency modeling, synergistically extracting temporal patterns and frequency components within dedicated architectures tailored for classification and forecasting tasks. Extensive experiments demonstrate that the proposed method significantly outperforms existing baselines on standard benchmarks such as UCR, yielding an average performance improvement of approximately 19.9% in both classification and forecasting.

Abstract

Time series analysis is fundamental in domains such as finance, healthcare, and meteorology. Real-world time series often exhibit multiscale characteristics shaped by diverse latent factors, resulting in intricate temporal patterns and rich frequency structures. However, existing approaches typically focus on either frequency-domain decomposition or time-domain pattern extraction in isolation, neglecting their joint structure. This decoupled modeling limits representation expressiveness and undermines performance in tasks requiring simultaneous temporal and spectral reasoning. To address this gap, we propose m-WCN, a novel end-to-end deep learning framework that neuralizes multi-wavelet decomposition for joint extraction of temporal patterns and frequency components. By approximating the classical GHM multi-wavelet transform with trainable convolutional operators and enforcing orthogonality constraints, m-WCN produces interpretable multi-resolution representations. Built on this foundation, we introduce two task-specific architectures: TFBC for time series classification, which boosts discriminative features across frequency scales, and FTB for forecasting, which ensembles frequency-aware predictors. Extensive experiments on 64 UCR datasets and seven public forecasting benchmarks demonstrate the effectiveness of our approach. Built on the neuralized m-WCN, our TFBC and FTB outperform various baseline models across diverse datasets, achieving average improvements of 19.97% in classification and 19.92% in forecasting tasks.

Problem

• Time Series Classification
• Time Series Forecasting
• Multi-Wavelet Decomposition
• Multiscale Representation
• Joint Time-Frequency Modeling

Innovation

• Multi-wavelet decomposition
• Neuralized wavelet transform
• Time series classification
• Time series forecasting
• Orthogonality constraints