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How can we detect fraudulent lockstep behavior in large-scale multi-aspect data (i.e., tensors)? Can we detect it when data are too large to fit in memory or even on a disk? Past studies have shown that dense subtensors in real-world tensors (e.g., social media, Wikipedia, TCP dumps, etc.) signal anomalous or fraudulent behavior such as retweet boosting, bot activities, and network attacks. Thus, various approaches, including tensor decomposition and search, have been proposed for detecting dense subtensors rapidly and accurately. However, existing methods suffer from low accuracy, or they assume that tensors are small enough to fit in main memory, which is unrealistic in many real-world applications such as social media and web. To overcome these limitations, we propose  D-Cube , a disk-based dense-subtensor detection method, which also can run in a distributed manner across multiple machines. Compared to state-of-the-art methods,  D-Cube  is (1) Memory Efficient: requires up to  1,561× less memory  and handles  1,000× larger  data ( 2.6TB ), (2) Fast: up to  7× faster  due to its near-linear scalability, (3) Provably Accurate: gives a guarantee on the densities of the detected subtensors, and (4) Effective: spotted network attacks from TCP dumps and synchronized behavior in rating data most accurately.

Detecting Group Anomalies in Tera-Scale Multi-Aspect Data via Dense-Subtensor Mining