Time series analysis is a fundamental task in various application domains, and deep learning approaches have demonstrated remarkable performance in this area. However, many real-world time series data exhibit significant periodic or quasi-periodic dynamics that are often not adequately captured by existing deep learning-based solutions. This results in an incomplete representation of the underlying dynamic behaviors of interest. To address this gap, we propose an unsupervised method called Floss that automatically regularizes learned representations in the frequency domain. The Floss method first automatically detects major periodicities from the time series. It then employs periodic shift and spectral density similarity measures to learn meaningful representations with periodic consistency. In addition, Floss can be easily incorporated into both supervised, semi-supervised, and unsupervised learning frameworks. We conduct extensive experiments on common time series classification, forecasting, and anomaly detection tasks to demonstrate the effectiveness of Floss. We incorporate Floss into several representative deep learning solutions to justify our design choices and demonstrate that it is capable of automatically discovering periodic dynamics and improving state-of-the-art deep learning models.

翻译：时间序列分析是众多应用领域中的基础任务，深度学习方法在此领域已展现出卓越性能。然而，许多真实世界的时间序列数据具有显著的周期性或准周期动态特性，现有基于深度学习的方案通常未能充分捕捉这些特征，导致对感兴趣潜在动态行为的表征不完整。针对这一不足，我们提出一种名为Floss的无监督方法，该方法可在频域中对学习到的表示进行自动正则化。Floss方法首先从时间序列中自动检测主要周期，随后通过周期移位与谱密度相似度度量，学习具有周期一致性的有意义表示。此外，Floss可轻松集成到监督、半监督及无监督学习框架中。我们针对常见的时间序列分类、预测和异常检测任务开展了广泛实验，以验证Floss的有效性。将Floss嵌入多个代表性深度学习方案后，我们验证了设计选择的合理性，并证明其能够自动发现周期动态特性，从而改进当前最先进的深度学习模型。