MLOW: Interpretable Low-Rank Frequency Magnitude Decomposition of Multiple Effects for Time Series Forecasting

2026-03-18

AI Summary

This work addresses the challenge that existing time series forecasting models struggle to achieve interpretable decomposition of multiple effects—such as trend and seasonality—using time-domain smoothing methods. The authors propose MLOW, an interpretable decomposition framework grounded in the frequency domain’s amplitude spectrum, which captures dominant effects through low-rank representations. To mitigate spectral leakage, MLOW incorporates a flexible mechanism for input windowing and frequency selection. Its core innovation is Hyperplane Non-negative Matrix Factorization (Hyperplane-NMF), which balances interpretability with computational efficiency and generalization. MLOW enables hierarchical, noise-robust multi-effect decomposition and can be seamlessly integrated as a plug-and-play module into mainstream forecasting architectures. Experimental results across multiple benchmarks demonstrate significant performance gains with minimal modifications, while visualizations confirm the clarity and validity of its decompositions.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Separating multiple effects in time series is fundamental yet challenging for time-series forecasting (TSF). However, existing TSF models cannot effectively learn interpretable multi-effect decomposition by their smoothing-based temporal techniques. Here, a new interpretable frequency-based decomposition pipeline MLOW captures the insight: a time series can be represented as a magnitude spectrum multiplied by the corresponding phase-aware basis functions, and the magnitude spectrum distribution of a time series always exhibits observable patterns for different effects. MLOW learns a low-rank representation of the magnitude spectrum to capture dominant trending and seasonal effects. We explore low-rank methods, including PCA, NMF, and Semi-NMF, and find that none can simultaneously achieve interpretable, efficient and generalizable decomposition. Thus, we propose hyperplane-nonnegative matrix factorization (Hyperplane-NMF). Further, to address the frequency (spectral) leakage restricting high-quality low-rank decomposition, MLOW enables a flexible selection of input horizons and frequency levels via a mathematical mechanism. Visual analysis demonstrates that MLOW enables interpretable and hierarchical multiple-effect decomposition, robust to noises. It can also enable plug-and-play in existing TSF backbones with remarkable performance improvement but minimal architectural modifications.

Problem

• time series forecasting
• interpretable decomposition
• multi-effect separation
• frequency magnitude spectrum
• low-rank representation

Innovation

• frequency-based decomposition
• low-rank magnitude spectrum
• Hyperplane-NMF
• spectral leakage mitigation
• interpretable time series forecasting