Group-Sparse Differential Reweighted Latent Matrix Factorization for Consistency Completion Under Non-Uniform Sensor Failures

In the contemporary industrial landscape, the widespread deployment of data collection units has become the standard, significantly enhancing the synchronization of data-driven control and monitoring systems. However, high noise levels and sensor failures frequently lead to non-uniform data loss, including random and block missing, which severely hinders the real-time integration of communication in sampling processes. To address this challenge, we propose a missing data completion method based on group-sparse differential reweighted latent matrix factorization (GSDRMF). The proposed method mitigates the impact of noise and sparse outliers on the global piecewise smoothness of the data by incorporating Frobenius and sparse norm constraints, enabling more precise rank approximation. In the low-rank approximation phase, we employ Burer-Monteiro nonconvex reweighted factorization to estimate the rank of the partially observed matrix. Simultaneously, leveraging temporal consistency, a group-sparse norm constraint is applied to the temporal gradient of the latent matrix. Finally, using a dual nonconvex alternating direction method of multipliers (ADMMs) optimization algorithm embedded with fast Fourier transform (FFT), the optimized latent variables are efficiently computed to meet optimality conditions while accelerating the overall computation speed. The proposed method is validated through its application to two real-world industrial processes, demonstrating its effectiveness in handling both non-uniform random and block missing data.