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Time series analysis is a fundamental task in various application domains,and deep learning approaches have demonstrated remarkable performance in thisarea. However, many real-world time series data exhibit significant periodic orquasi-periodic dynamics that are often not adequately captured by existing deeplearning-based solutions. This results in an incomplete representation of theunderlying dynamic behaviors of interest. To address this gap, we propose anunsupervised method called Floss that automatically regularizes learnedrepresentations in the frequency domain. The Floss method first automaticallydetects major periodicities from the time series. It then employs periodicshift and spectral density similarity measures to learn meaningfulrepresentations with periodic consistency. In addition, Floss can be easilyincorporated into both supervised, semi-supervised, and unsupervised learningframeworks. We conduct extensive experiments on common time seriesclassification, forecasting, and anomaly detection tasks to demonstrate theeffectiveness of Floss. We incorporate Floss into several representative deeplearning solutions to justify our design choices and demonstrate that it iscapable of automatically discovering periodic dynamics and improvingstate-of-the-art deep learning models.

Enhancing Representation Learning for Periodic Time Series with Floss: A Frequency Domain Regularization Approach