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

Xuke Wu^1,2Lan Wang^2,3Miao Ge^1,4Jing Jiang^1,4Yu Cai¹Bing Yang^1,4*

• ¹Chongqing Eco-Environment Monitoring Center, Chongqing, China
• ²School of Computer Science & Technology, Chongqing University of Posts and Telecommunications, Chongqing, Chongqing, China
• ³Chongqing University of Education, Chongqing, Chongqing, China
• ⁴School of Environment and Ecology, Chongqing University, Chongqing, China

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 can provide a wealth of spatiotemporally data to water authorities. Yet large-scale missing data in wireless sensor-based networks seems inevitable owing to various reasons. Massive missing data may raise rigorous concerns in downstream mathematic modeling and statistical decisions, leading to misjudgments in the risk assessment of water quality. A high-dimensional and incomplete (HDI) tensor can specifically quantify multi-sensor data. Moreover, a latent factorization of tensors (LFT) model effectively extracts multivariate dependencies and spatiotemporal correlations hidden in such an HDI tensor, achieving high-accuracy missing data imputation. However, it fails to adequately account for inherent fluctuations of water quality data, thereby limiting its representation learning ability. Empirical evidence indicates that incorporating bias schemes into learning models can effectively mitigate their underfitting. Building on this insight, we meticulously investigate the performance gains brought by bias schemes to an LFT model. Subsequently, this work proposes an adaptive biases-incorporated LFT (ABL) model with four-fold ideas: incorporating basic linear biases for describing constant fluctuations of water quality data, designing weighted pretraining biases for obtaining historical prior information of data fluctuations, utilizing time-aware biases for capturing long-term patterns of water quality fluctuations, and performing hyper-parameter adaptation following the principle of particle swarm optimization (PSO) for achieving a practical model. Empirical studies on large-scale water quality datasets from real applications demonstrate that compared with state-of-the-art models, the proposed ABL realizes significant gains in prediction accuracy and computational efficiency.