  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.
