  The network traffic matrix is widely used in network operation and
management. It is therefore of crucial importance to analyze the components and
the structure of the network traffic matrix, for which several mathematical
approaches such as Principal Component Analysis (PCA) were proposed. In this
paper, we first argue that PCA performs poorly for analyzing traffic matrix
that is polluted by large volume anomalies, and then propose a new
decomposition model for the network traffic matrix. According to this model, we
carry out the structural analysis by decomposing the network traffic matrix
into three sub-matrices, namely, the deterministic traffic, the anomaly traffic
and the noise traffic matrix, which is similar to the Robust Principal
Component Analysis (RPCA) problem previously studied in [13]. Based on the
Relaxed Principal Component Pursuit (Relaxed PCP) method and the Accelerated
Proximal Gradient (APG) algorithm, we present an iterative approach for
decomposing a traffic matrix, and demonstrate its efficiency and flexibility by
experimental results. Finally, we further discuss several features of the
deterministic and noise traffic. Our study develops a novel method for the
problem of structural analysis of the traffic matrix, which is robust against
pollution of large volume anomalies.
