# Multilevel Wavelet Decomposition Network for Interpretable Time Series Analysis

arXiv: https://arxiv.org/abs/1806.08946 · HTML: https://mlsanity.com/paper/1806.08946/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2018.

## Built on by (most cited first, 30 of 61)

- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting](https://mlsanity.com/paper/2205.08897/) (2022)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [A Survey on Deep Learning based Time Series Analysis with Frequency Transformation](https://mlsanity.com/paper/2302.02173/) (2023)
- [Adaptive wavelet distillation from neural networks through interpretations](https://mlsanity.com/paper/2107.09145/) (2021)
- [Universal Time-Series Representation Learning: A Survey](https://mlsanity.com/paper/2401.03717/) (2024)
- [Fully Learnable Deep Wavelet Transform for Unsupervised Monitoring of High-Frequency Time Series](https://mlsanity.com/paper/2105.00899/) (2021)
- [Out-of-Distribution Generalization in Time Series: A Survey](https://mlsanity.com/paper/2503.13868/) (2025)
- [Spatial-Temporal Interactive Dynamic Graph Convolution Network for Traffic Forecasting](https://mlsanity.com/paper/2205.08689/) (2022)
- [Benchmarking Online Sequence-to-Sequence and Character-based Handwriting Recognition from IMU-Enhanced Pens](https://mlsanity.com/paper/2202.07036/) (2022)
- [dCAM: Dimension-wise Class Activation Map for Explaining Multivariate Data Series Classification](https://mlsanity.com/paper/2207.12165/) (2022)
- [The Evolution of Reinforcement Learning in Quantitative Finance: A Survey](https://mlsanity.com/paper/2408.10932/) (2024)
- [Robust Time Series Denoising with Learnable Wavelet Packet Transform](https://mlsanity.com/paper/2206.06126/) (2022)
- [MetaTrader: An Reinforcement Learning Approach Integrating Diverse Policies for Portfolio Optimization](https://mlsanity.com/paper/2210.01774/) (2022)
- [Full Bayesian Significance Testing for Neural Networks](https://mlsanity.com/paper/2401.13335/) (2024)
- [XAI Methods for Neural Time Series Classification: A Brief Review](https://mlsanity.com/paper/2108.08009/) (2021)
- [Interpretability is a Kind of Safety: An Interpreter-based Ensemble for Adversary Defense](https://mlsanity.com/paper/2304.06919/) (2023)
- [Fusing Structure from Motion and Simulation-Augmented Pose Regression from Optical Flow for Challenging Indoor Environments](https://mlsanity.com/paper/2304.07250/) (2023)
- [Phase-driven Domain Generalizable Learning for Nonstationary Time Series](https://mlsanity.com/paper/2402.05960/) (2024)
- [Evaluation of (Un-)Supervised Machine Learning Methods for GNSS Interference Classification with Real-World Data Discrepancies](https://mlsanity.com/paper/2503.23775/) (2025)
- [Learning Universal Multi-level Market Irrationality Factors to Improve Stock Return Forecasting](https://mlsanity.com/paper/2502.04737/) (2025)
- [Revisiting Backdoor Attacks on Time Series Classification in the Frequency Domain](https://mlsanity.com/paper/2503.09712/) (2025)
- [Multi-Order Wavelet Derivative Transform for Deep Time Series Forecasting](https://mlsanity.com/paper/2505.11781/) (2025)
- [Taking ROCKET on an Efficiency Mission: Multivariate Time Series Classification with LightWaveS](https://mlsanity.com/paper/2204.01379/) (2022)
- [Edge-Varying Fourier Graph Networks for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2210.03093/) (2022)
- [Wavelet-Inspired Multiscale Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2401.06040/) (2024)
- [Disentangling Imperfect: A Wavelet-Infused Multilevel Heterogeneous Network for Human Activity Recognition in Flawed Wearable Sensor Data](https://mlsanity.com/paper/2402.09434/) (2024)
- [WEITS: A Wavelet-enhanced residual framework for interpretable time series forecasting](https://mlsanity.com/paper/2405.10877/) (2024)
- [Diffeomorphic Temporal Alignment Nets for Time-series Joint Alignment and Averaging](https://mlsanity.com/paper/2502.06591/) (2025)
- [A Novel Framework for Significant Wave Height Prediction based on Adaptive Feature Extraction Time-Frequency Network](https://mlsanity.com/paper/2505.06688/) (2025)

## Abstract (arXiv)

Recent years have witnessed the unprecedented rising of time series from almost all kindes of academic and industrial fields. Various types of deep neural network models have been introduced to time series analysis, but the important frequency information is yet lack of effective modeling. In light of this, in this paper we propose a wavelet-based neural network structure called multilevel Wavelet Decomposition Network (mWDN) for building frequency-aware deep learning models for time series analysis. mWDN preserves the advantage of multilevel discrete wavelet decomposition in frequency learning while enables the fine-tuning of all parameters under a deep neural network framework. Based on mWDN, we further propose two deep learning models called Residual Classification Flow (RCF) and multi-frequecy Long Short-Term Memory (mLSTM) for time series classification and forecasting, respectively. The two models take all or partial mWDN decomposed sub-series in different frequencies as input, and resort to the back propagation algorithm to learn all the parameters globally, which enables seamless embedding of wavelet-based frequency analysis into deep learning frameworks. Extensive experiments on 40 UCR datasets and a real-world user volume dataset demonstrate the excellent performance of our time series models based on mWDN. In particular, we propose an importance analysis method to mWDN based models, which successfully identifies those time-series elements and mWDN layers that are crucially important to time series analysis. This indeed indicates the interpretability advantage of mWDN, and can be viewed as an indepth exploration to interpretable deep learning.