Internet Traffic Matrix Structural Analysis Based on Multi-Resolution RPCA

Abstract: The Internet traffic matrix plays a significant roll in network operation and management, therefore, the structural analysis of traffic matrix, which decomposes different traffic components of this high-dimensional traffic dataset, is quite valuable to some network applications. In this study, based on the Robust Principal Component Analysis (RPCA) theory, a novel traffic matrix structural analysis approach named Multi-Resolution RPCA is created, which utilizes the wavelet multi-resolution analysis. Firstly, we build the Multi-Resolution Traffic Matrix Decomposition Model (MR-TMDM), which characterizes the smoothness of the deterministic traffic by its wavelet coefficients. Secondly, based on this model, we improve the Stable Principal Component Pursuit (SPCP), propose a new traffic matrix decomposition method named SPCP-MRC with Multi-Resolution Constraints, and design its numerical algorithm. Specifically, we give and prove the closed-form solution to a sub-problem in the algorithm. Lastly, we evaluate different traffic decomposition methods by multiple groups of simulated traffic matrices containing different kinds of anomalies and distinct noise levels. It is demonstrated that SPCP-MRC, compared with other methods, achieves more accurate and more reasonable traffic decompositions.