A Huber-Regularized Latent Factorization of Tensors Approach for Large-Scale Incomplete Water Quality Data Imputation

An online water quality monitoring network continuously collects multiple key water quality indicators across distributed monitoring sites via wireless sensors, providing essential data support for intelligent water resource management and ecological assessment. These large-scale observations can be naturally represented as a high-dimensional and incomplete (HDI) water quality tensor with frequent missing entries. Such an HDI tensor contains rich multivariate, spatial, and temporal dependencies that can be effectively exploited for missing data recovery. Latent factorization of tensors (LFT) models have demonstrated remarkable capability in extracting latent knowledge from HDI tensors, thereby enabling accurate missing data imputation. However, existing LFT models generally adopt the conventional L2 regularization scheme, making them highly sensitive to sensor outliers that are ubiquitous in real-time monitoring environments. To address this issue, this study proposes a Huber-regularized latent factorization of tensors (HRL) model under the Tucker decomposition framework. Specifically, a Huber regularization scheme is incorporated into the learning objective to improve robustness against outliers while preserving the smoothness of latent factor learning. Empirical studies on eight practical HDI water quality tensors demonstrate that the proposed HRL model consistently outperforms state-of-the-art models in terms of computational efficiency and imputation accuracy, offering an effective and robust solution for large-scale incomplete water quality data reconstruction and facilitating reliable downstream decision-making.