TopoCL: Topological Contrastive Learning for Time Series

Universal time-series representation learning is challenging but valuable in real-world applications such as classification, anomaly detection, and forecasting. Recently, contrastive learning (CL) has been actively explored to tackle time-series representation. However, a key challenge is that the data augmentation process in CL can distort seasonal patterns or temporal dependencies, inevitably leading to a loss of semantic information. To address this challenge, we propose topological CL for time series (TopoCL). TopoCL mitigates such information loss by incorporating persistent homology, which captures the topological characteristics of data that remain invariant under transformations. In this article, we treat the temporal and topological properties of time-series data as distinct modalities. Specifically, we compute persistent homology to construct topological features of time-series data, representing them in persistence diagrams (PDs). We then design a neural network to encode these persistent diagrams. Our approach jointly optimizes CL within the time modality and time-topology correspondence, promoting a comprehensive understanding of both temporal semantics and topological properties of time series. We conduct extensive experiments on four downstream tasks-classification, anomaly detection, forecasting, and transfer learning. The results demonstrate that TopoCL achieves state-of-the-art performance.