Fast Tensor Factorization for Accurate Internet Anomaly Detection

Detecting anomalous traffic is a critical task for advanced Internet management. Many anomaly detection algorithms have been proposed recently. However, constrained by their matrix-based traffic data model, existing algorithms often suffer from low accuracy in anomaly detection. To fully utilize the multi-dimensional information hidden in the traffic data, this paper takes the initiative to investigate the potential and methodologies of performing tensor factorization for more accurate Internet anomaly detection. More specifically, we model the traffic data as a three-way tensor and formulate the anomaly detection problem as a robust tensor recovery problem with the constraints on the rank of the tensor and the cardinality of the anomaly set. These constraints, however, make the problem extremely hard to solve. Rather than resorting to the convex relaxation at the cost of low detection performance, we propose TensorDet to solve the problem directly and efficiently. To improve the anomaly detection accuracy and tensor factorization speed, TensorDet exploits the factorization structure with two novel techniques, sequential tensor truncation and two-phase anomaly detection. We have conducted extensive experiments using Internet traffic trace data Abilene and GÈANT. Compared with the state of art algorithms for tensor recovery and matrix-based anomaly detection, TensorDet can achieve significantly lower false positive rate and higher true positive rate. Particularly, benefiting from our well designed algorithm to reduce the computation cost of tensor factorization, the tensor factorization process in TensorDet is 5 (Abilene) and 13 (GÈANT) times faster than that of the traditional Tucker decomposition solution.