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The ubiquitous 5G-enable industrial Internet of Things interconnects a great number of intelligent sensors and actors. Network management becomes challenging due to massive traffic data generated by industrial equipment. However, the conventional single traffic factor is insufficient for the increasingly complicated network engineering tasks due to the poor representation capability. Besides, the insecure equipment with open communication access easily brings irregular network fluctuations to network traffic which interferes with the primary traffic factor. The simple and interfered traffic factor decreases the network management efficiency and misleads the operators. Motivated by that, we construct a comprehensive tensor model representing multi-dimension traffic factors to describe the network traffic beneficial characteristics. Meanwhile, an adaptive and generic low-rank tensor recovery (AG-LRTR) algorithm in the tensor singular value decomposition (t-SVD) framework is proposed for denoising. For effective tensor recovery, the alternating direction method of multipliers is employed to theoretically solve the partial augmented Lagrangian function of our objective with a closed-form solution. Numerical experiments on both synthetic data and real-world traffic data in IIoT validate that our proposed algorithm outperforms other state-of-the-art of tensor recovery algorithms.

Tensor decomposition is widely used to exploit the internal correlation in multi-way data analysis and process for communications and radar systems. As one of the main tensor decomposition methods, CANDECOMP/PARAFAC decomposition has advantages of uniqueness and interpretation properties which are significant in practical applications. However, traditional decomposition method is sensitive to both predefined rank and noise that results in inaccurate tensor decomposition. In this paper, we propose a improved algorithm called the Element-wise Average Alternating Direction Method of Multipliers by minimizing the sum of all factors’ trace norm and the noise variance. Our algorithm could overcome the dependence on predefined rank in traditional decomposition algorithms and alleviate the impact of noise. Moreover, this algorithm can be transferred to solve the problem of tensor completion conveniently. The simulation results show that our proposed algorithm could decompose the noisy tensor to the factors with above 90% similarity in various SNR and also interpolate the incomplete tensor with higher similar coefficient and lower relative reconstruction error when the missing rate is less than 0.5.

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