Internet traffic tensor completion with tensor nuclear norm

The incomplete data is a common phenomenon in traffic network because of the high measurement cost, the failure of data collection systems and unavoidable transmission loss. Recovering the whole data from incomplete data is a very important task in internet engineering and management. In this paper, we adopt the low-rank tensor completion model equipped with tensor nuclear norm to reconstruct the internet traffic data. Besides using a low rank tensor to capture the global information of internet traffic data, we also utilize spatial correlation and periodicity to characterize the local information. The resulting model is a convex and separable optimization. Then, a proximal alternating direction method of multipliers is customized to solve the optimization problem, where all subproblems have closed-form solutions. Convergence analysis of the algorithm is given without any assumptions. Numerical experiments on Abilene and GeANT datasets with random missing and structured loss show that the proposed model and algorithm perform better than other existing algorithms.