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

TL;DR

MLOW introduces a frequency-based, interpretable low-rank decomposition method for time series forecasting that captures multiple effects and improves performance with minimal architectural changes.

Contribution

It proposes Hyperplane-NMF for interpretable low-rank spectrum decomposition and a flexible mechanism for frequency selection, addressing spectral leakage issues.

Findings

MLOW achieves interpretable, hierarchical effect decomposition.

It demonstrates robustness to noise in time series.

Provides significant performance improvements with minimal modifications.

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.