Omni-Dimensional Frequency Learner for General Time Series Analysis

TL;DR

ODFL introduces a general-purpose time series model that leverages spectral features along the channel, frequency, and variable dimensions. By applying a semantic-adaptive, sparse, partial-channel filter in the frequency domain and mapping back to the time domain, it achieves state-of-the-art performance across forecasting, imputation, classification, and anomaly detection. The work demonstrates significant gains over strong baselines, supports robustness via ablations and noise tests, and highlights the value of representation learning for further improvements. This approach offers a practical, scalable foundation for broad-time-series analysis with potential for extensive self-supervised pretraining.

Abstract

Frequency domain representation of time series feature offers a concise representation for handling real-world time series data with inherent complexity and dynamic nature. However, current frequency-based methods with complex operations still fall short of state-of-the-art time domain methods for general time series analysis. In this work, we present Omni-Dimensional Frequency Learner (ODFL) model based on a in depth analysis among all the three aspects of the spectrum feature: channel redundancy property among the frequency dimension, the sparse and un-salient frequency energy distribution among the frequency dimension, and the semantic diversity among the variable dimension. Technically, our method is composed of a semantic-adaptive global filter with attention to the un-salient frequency bands and partial operation among the channel dimension. Empirical results show that ODFL achieves consistent state-of-the-art in five mainstream time series analysis tasks, including short- and long-term forecasting, imputation, classification, and anomaly detection, offering a promising foundation for time series analysis.

Figures (8)

• Figure 1: Illustration of (a) the baseline operator, (b) the partial operation, (c) the unsalient frequency bands feature extraction, (d) the semantic diversity and adaptation under the channel independent setting.
• Figure 2: Visualization of channel redundancy in the frequency domain. Only the real part is visualized. Qualitatively, we can see the high redundancies across different channels.
• Figure 3: The architecture of our proposed method. The transformed frequency feature is firstly partial to two parts. Then, our learned adaptive filter is applied on only a few inputs channels and the unsalient frequency bands while leaving the remaining ones untouched. For simplicity, we only take one variable example for visualization.
• Figure 4: The effective dimension ratio $r_{d(0.8)}$ of our model which reflects the feature redundant and diversity. Higher effective dimension ratio indicates more diverse feature among channel dimension.
• Figure 5: Model comparison in classification. The results are averaged from 10 subsets of UEA. Higher accuracy indicates better performance. See Table \ref{['tab:full_classification_results']} in Appendix \ref{['appendix:full']} for full results.