A Barzilai–Borwein Gradient Algorithm for Spatio-Temporal Internet Traffic Data Completion via Tensor Triple Decomposition

With the coming of high-speed network and 5G era, internet traffic data is crucial for various network tasks such as traffic engineering, capacity planning and anomaly detection. To explore the natural spatio-temporal structure of network flow, we use the novel triple decomposition of tensors to establish an optimization model with the spatio-temporal regularization for completing the internet traffic data. A Barzilai–Borwein gradient algorithm is designed for solving the spatio-temporal internet traffic tensor completion problem. We prove the convergence of this algorithm and analyze its convergence rate with the tool of the Kurdyka-Łojasiewicz property. Numerical experiments on Abilene and GEANT datasets report that the proposed tensor completion method is effective.