Graph spectral filtering-enhanced tensor completion based on Schatten-p norm for missing measurements recovery with noise

Graph Neural Networks (GNNs) have shown state-of-the-art (SOTA) performance in intelligent fault diagnosis and prognosis. However, their real-world deployment is often hindered by incomplete and noisy sensor data. Existing Tensor Completion (TC) methods fall short by overlooking the spectral filtering properties intrinsic to GNNs. In this paper, we propose Graph Spectral Filtering-enhanced Tensor Completion (GSFTC), a novel method that leverages GNN graph spectral filtering properties to enhance feature propagation under data corruption. By modeling the signal as a combination of pure and noise components, the tensor completion task is formulated as a non-convex rank minimization problem with two spectral-aware regularizers. Subsequently, it is solved alternately via proximal block coordinate descent method. Extensive experiments on five diagnostic and prognostic datasets demonstrate that GSFTC consistently outperforms SOTA iterative-based methods in restoring model performance under varying completion rates, noise levels, and missingness patterns. In particular, GSFTC achieves notable robustness to noise and significant improvements under data imbalance, with up to 94.62% and 49.28% gains in F₁ score under random and structural missingness, respectively, on the XJTULRE dataset. The observed performance improvements are validated experimentally and can be attributed to GSFTC’s effective preservation and recovery of informative feature propagation across GNN layers through graph spectral filtering. Specifically, the scalability of GSFTC is partly constrained by its computational complexity and limited ability to handle structural missingness. Future extensions leveraging deep unfolding could integrate TC priors with parameterized learning to reduce complexity while maintaining accuracy. The source code is publicly available at https://github.com/zhirongzhong/GSFTC .