Internet traffic data recovery via a low-rank spatio-temporal regularized optimization approach without d-th order T-SVD

Yuxuan Duan¹Chen Ling²Jinjie Liu^1*Xinmin Yang¹

• ¹National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chongqing, China
• ²Department of Mathematics, Hangzhou Dianzi University,, Hangzhou, China

Accurate recovery of Internet traffic data can mitigate the adverse impact of incomplete data on network task processes. In this paper, we propose a low-rank recovery model for incomplete Internet traffic data with a fourth-order tensor structure, incorporating spatio-temporal regularization while avoiding the use of d-th order T-SVD. Based on d-th order tensor product, we first establish the equivalence between d-th order tensor nuclear norm and the minimum sum of the squared Frobenius norms of two factor tensors under the unitary transformation domain. This equivalence allows us to leave aside the d-th order T-SVD, significantly reducing the computational complexity of solving the problem. Additionally, we integrate the alternating direction method of multipliers (ADMM) to design an efficient and stable algorithm for precise model solving. Finally, we validate the proposed approach by simulating scenarios with random and structured missing data on two real-world Internet traffic datasets. Experimental results demonstrate that our method exhibits significant advantages in data recovery performance compared to existing methods.