M-Zoom: Fast Dense-Block Detection in Tensors with Quality Guarantees

Abstract

Given a large-scale and high-order tensor, how can we find dense blocks in it? Can we find them in near-linear time but with a quality guarantee? Extensive previous work has shown that dense blocks in tensors as well as graphs indicate anomalous or fraudulent behavior e.g., lockstep behavior in social networks. However, available methods for detecting such dense blocks are not satisfactory in terms of speed, accuracy, or flexibility. In this work, we propose M-Zoom, a flexible framework for finding dense blocks in tensors, which works with a broad class of density measures. M-Zoom has the following properties: 1 Scalable: M-Zoom scales linearly with all aspects of tensors and is upi¾źto 114$$\times $$faster than state-of-the-art methods with similar accuracy. 2 Provably accurate: M-Zoom provides a guarantee on the lowest density of the blocks it finds. 3 Flexible: M-Zoom supports multi-block detection and size bounds as well as diverse density measures. 4 Effective: M-Zoom successfully detected edit wars and bot activities in Wikipedia, and spotted network attacks from a TCP dump with near-perfect accuracy AUCi¾ź=i¾ź0.98. The data and software related to this paper are available at http://www.cs.cmu.edu/~kijungs/codes/mzoom/.