Adaptive biases-incorporated latent factorization of tensors for predicting missing data in water quality monitoring networks

Real-time monitoring of key water quality parameters is essential for the scientific management and effective maintenance of aquatic ecosystems. Water quality monitoring networks equipped with multiple low-cost electrochemical and optical sensors generate abundant spatiotemporal data for water authorities. However, large-scale missing data in wireless sensor networks is inevitable due to various factors, which may introduce uncertainties in downstream mathematical modeling and statistical decisions, potentially leading to misjudgments in water quality risk assessment. A high-dimensional and incomplete (HDI) tensor can specifically quantify multi-sensor data, and latent factorization of tensors (LFT) models effectively extract multivariate dependencies and spatiotemporal correlations hidden in such a tensor to achieve high-accuracy missing data imputation. Nevertheless, LFT models fail to adequately account for the inherent fluctuations in water quality data, limiting their representation learning ability. Empirical evidence suggests that incorporating bias schemes into learning models can effectively mitigate underfitting. Building on this insight, this study proposes an adaptive biases-incorporated LFT (ABL) model with four-fold ideas: basic linear biases to describe constant fluctuations in water quality data; weighted pretraining biases to capture historical prior information of data fluctuations; time-aware biases to model long-term patterns of water quality fluctuations; and hyperparameter adaptation via particle swarm optimization (PSO) to enhance practicality. Empirical studies on large-scale real-world water quality datasets demonstrate that the proposed ABL model achieves significant improvements in both prediction accuracy and computational efficiency compared with state-of-the-art models. The findings highlight that integrating multiple bias schemes into tensor factorization models can effectively address the limitations of existing LFT models in capturing inherent data fluctuations, thereby enhancing the reliability of missing data imputation for water quality monitoring. This advancement contributes to more robust downstream applications in water quality management and risk assessment.