A nonlinear low-rank representation model with convolutional neural network for imputing water quality data

The integrity of Water Quality Data (WQD) is critical in environmental monitoring for scientific decision-making and ecological protection. However, water quality monitoring systems are often challenged by large amounts of missing data due to unavoidable problems such as sensor failures and communication delays, which further lead to water quality data becoming High-Dimensional and Sparse (HDS). Traditional data imputation methods are difficult to depict the potential dynamics and fail to capture the deep data features, resulting in unsatisfactory imputation performance. To effectively solve this limitation, this paper proposes a Nonlinear Low-rank Representation model (NLR) with Convolutional Neural Networks (CNN) for imputing missing WQD, which utilizes CNNs to implement two ideas: a) fusing temporal features to model the temporal dependence of data between time slots, and b) Extracting nonlinear interactions and local patterns to mine higher-order relationships features and achieve deep fusion of multidimensional information. Experimental studies on three real water quality datasets show that the NLR-CNN model outperforms existing state-of-the-art imputation models in estimation accuracy. It provides an effective and reliable approach for handling water quality monitoring data, especially in complex and dynamic environmental conditions.