Waven-Pull: Wavelet-based Anomaly Detection in Dynamic Graphs via Positive-Unlabeled Learning

ICLR 2026 Conference Submission8881 Authors

Keywords: Anomaly detection, dynamic graphs, positive-unlabeled learning

Abstract: Anomaly detection in dynamic graphs is vital for identifying evolving threats in domains such as social networks and financial systems. While Graph Neural Networks (GNNs) have shown promise, they typically require ample labeled data (both normal and anomalous) to distinguish anomalous nodes from normal ones. In practice, however, only a small subset of anomalies are labeled, leaving most nodes unlabeled, a scenario known as positive-unlabeled (PU) learning. This, combined with the oversmoothing tendency of GNNs, leads to a strong bias toward predicting most nodes as normal, thus severely limiting detection performance. To address these challenges, we propose WAVEN-PULL: WAVElet-based ANomaly detection in dynamic graphs via Positive-Unlabeled Learning. WAVEN-PULL features: (1) dynamic graph encoder that combines Beta-Wavelet Graph Convolution and temporal attention to capture multi-scale spectral patterns and the temporal evolution of node behaviors, thereby effectively capturing anomalous signals in dynamic graphs and mitigating oversmoothing; (2) PU-aware alignment module that corrects prediction bias by aligning the anomaly ratio of unlabeled predictions with class priors, which can be theoretically shown to yield an unbiased risk estimator with temporal stability under exponential moving average (EMA); and (3) anomaly probability estimation module that maps node embeddings to probabilities, ensuring consistency with risk minimization principles and enabling robust end-to-end detection even with scarce labels. Extensive experiments on real-world dynamic graph datasets demonstrate that WAVEN-PULL consistently outperforms state-of-the-art methods, achieving absolute AUC improvements of 6.15%, 22.81%, and 4.74% on Wikipedia, Reddit, and Bit-Alpha, respectively.

Primary Area: learning on graphs and other geometries & topologies

Submission Number: 8881