Abstract：In the network system, data missing cannot be avoided regardless of the traffic measurement systems. To solve the problem of missing network traffic data, we propose a spatio-temporal tensor completion algorithm based on alternating least squares (ALS) to recover the missing values in the traffic data tensor. The proposed algorithm not only utilizes tensor decomposition and its low-dimensional representation, but also fully considers the spatio-temporal correlation of network traffic data, and further improves the accuracy of data recovery. This paper uses the Abilene dataset to test the algorithm and compares it to the state-of-the-art completion methods. The experimental results show that the proposed method can effectively reduce the error of traffic data recovery and improve the accuracy of data recovery.
[1] Roughan M, Thorup M, Zhang Y.Traffic engineering with estimated traffic matrices[C]//Proceedings of the 3rd ACM SIGCOMM Conference on Internet Measurement, 2003: 248-258. [2] Cahn R S.Wide area network design: concepts and tools for optimization[M]. USA: Morgan Kaufmann, 1998. [3] Lakhina A, Papagiannaki K, Crovella M, et al.Structural analysis of network traffic flows[C]// Proceedings of the Joint International Conference on Measurement and Modeling of Computer Systems, 2004: 61-72. [4] 闭小梅, 闭瑞华. KNN算法综述[J]. 科技创新导报, 2009(14): 31. [5] Roughan M, Zhang Y, Willinger W, et al.Spatio- temporal compressive sensing and Internet traffic matrices (extended version)[J]. IEEE/ACM Transa- ctions on Networking (ToN), 2012, 20(3): 662-676. [6] Cai J F, Candès E J, Shen Z.A singular value thresholding algorithm for matrix completion[J]. SIAM Journal on Optimization, 2010, 20(4): 1956-1982. [7] Jain P, Oh S.Provable tensor factorization with missing data[C]//Advances in Neural Information Processing Systems, 2014: 1431-1439. [8] Xu Y, Hao R, Yin W, et al.Parallel matrix factorization for low-rank tensor completion[J].Inverse Problems and Imaging, 2015, 9(2): 601-624. [9] 刘根兰, 倪永年. 荧光光谱法结合多元曲线分辨-交替最小二乘法研究伞形花内酯与牛血清白蛋白的相互作用[J]. 高等学校化学学报, 2008, 29(7): 1339-1343. [10] 王振军, 黄瑞章. 基于Spark的矩阵分解与最近邻融合的推荐算法[J]. 计算机系统应用, 2017, 26(4): 124-129. [11] Lin Kaitong, Zheng Haifeng, Feng Xinxin, et al.A novel Spatial-Temporal regularized tensor completion algorithm for traffic data imputation[C]//2018 10th International Conference on Wireless Communi- cations and Signal Processing (WCSP), 2018: 1-6. [12] Kilmer M E, Martin C D.Factorization strategies for third-order tensors[J]. Linear Algebra and Its Appli- cations, 2011, 435(3): 641-658. [13] Anandkumar A, Ge R, Hsu D, et al.Tensor decom- positions for learning latent variable models[J]. The Journal of Machine Learning Research, 2014, 15(1): 2773-2832. [14] “Abilene/internet2.”[EB/OL]. http://www.internet2.edu/.
2019, Vol. 20 
