Multi-low-rank Approximation for Traffic Matrices

With the Internet applications become more complex and diverse, simple network traffic matrix estimation or approximation methods such as gravity model are no longer adequate. In this paper, we advocate a novel approach of approximating traffic matrices with multiple low-rank matrices. We build the theory behind the MULTI-LOW-RANK approximation and discuss the conditions under which it is better than Low-Rank SVD in terms of both matrix approximation and preserving the local (and global) structure of the traffic matrices. Further, we develop an effective technique based on spectral clustering of column/row feature vectors for decomposing traffic matrices into multiple low rank matrices. We perform a series of experiments on traffic matrices extracted from a synthetic dataset and two real world datasets – one that represents nationwide cellular traffic and another taken from a tier-1 ISP. The results thus obtained show that: 1) MULTI-LOW-RANK approximation is superior for traffic classification; 2) it can be used to predict complete or missing entries of traffic matrices over time; 3) show it's robustness against noise; and 4) demonstrate that it closely follows the optimal solution (i.e., low-rank SVD solution).