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With the rapid growth of data communications in size and complexity, the threat of malicious activities and computer crimes has increased accordingly as well. Thus, investigating efficient data processing techniques for network operation and management over large-scale network traffic is highly required. Some mathematical approaches on flow-level traffic data have been proposed due to the importance of analyzing the structure and situation of the network. Different from the state-of-the-art studies, we first propose a new decomposition model based on accelerated proximal gradient method for packet-level traffic data. In addition, we present the iterative scheme of the algorithm for network anomaly detection problem, which is termed as NAD-APG. Based on the approach, we carry out the intrusion detection for packet-level network traffic data no matter whether it is polluted by noise or not. Finally, we design a prototype system for network anomalies detection such as Probe and R2L attacks. The experiments have shown that our approach is effective in revealing the patterns of network traffic data and detecting attacks from large-scale network traffic. Moreover, the experiments have demonstrated the robustness of the algorithm as well even when the network traffic is polluted by the large volume anomalies and noise

A Large-Scale Network Data Analysis via Sparse and Low Rank Reconstruction