CatchCore: Catching Hierarchical Dense Subtensor.

Dense subtensor detection gains remarkable success in spotting anomaly and fraudulent behaviors for the multi-aspect data (i.e., tensors), like in social media and event streams. Existing methods detect the densest subtensors flatly and separately, with an underlying assumption that these subtensors are exclusive. However, many real-world scenario usually present hierarchical properties, e.g., the core-periphery structure or dynamic communities in networks. In this paper, we propose CatchCore, a novel framework to effectively find the hierarchical dense subtensors. We first design a unified metric for dense subtensor detection, which can be optimized with gradient-based methods. With the proposed metric, CatchCore detects hierarchical dense subtensors through the hierarchy-wise alternative optimization. Finally, we utilize the minimum description length principle to measure the quality of detection result and select the optimal hierarchical dense subtensors. Extensive experiments on synthetic and real-world datasets demonstrate that CatchCore outperforms the top competitors in accuracy for detecting dense subtensors and anomaly patterns. Additionally, CatchCore identified a hierarchical researcher co-authorship group with intense interactions in DBLP dataset. Also CatchCore scales linearly with all aspects of tensors.