Multilinear Plus Sparse based Tensor Completion for Long-Term Operating Large-Scale and Heterogeneous Sensor Networks

Data integrity and correctness are essential for many internet of things applications. This work addresses the data completion problem for long-term operating, large-scale and heterogeneous wireless sensor networks (WSNs), using tensor completion technique. In most previous works, the data models only involve single temporal and single spatial dimensions, ignoring the higher-order intrinsic structures. Besides, most existing schemes use low-rankness and sparsity in a fixed domain to describe the data correlation, but neither can fit well with all the temporal, spatial and attribute correlation. To address these issues, we first propose a higher-order tensor model for data from WSNs, namely multilinear plus sparse (MPS) model, which has multiple temporal, multiple spatial and one attribute modes. The core idea is to describe the temporal-spatial-attribute correlation by the sparsity in the multilinear transform domain. Appropriate sparsifying transforms can be flexibly determined according to the specific natures of each mode. For the temporal and spatial modes, analytical transforms are adopted considering computational efficiency and addressing continuity feature. For the attribute mode, we utilize MPS to propose a robust $\ell _{0}$ -norm based principle component analysis (robust $\ell _{0}$ -PCA) algorithm to adaptively learn the sparsifying transform for various heterogeneous networks. Finally, based on MPS and the learned transform, we develop an efficient tensor completion algorithm using alternating direction method of multipliers, namely MPS-TC. The experimental results on real-life WSN data verify that the proposed robust $\ell _{0}$ -PCA algorithm can learn an attribute transform more robustly than the conventional PCA and $\ell _{1}$ -PCA algorithms; and the proposed MPS-TC algorithm outperforms the state-of-the-art tensor completion algorithms in terms of signal-to-noise ratio and root mean square error.