A Causal Convolutional Low-rank Representation Model for Imputation of Water Quality Data

TL;DR

This work tackles missing values in High-Dimensional and Sparse water quality data by introducing CLR, a causal convolutional low-rank representation that fuses temporal information into a CPD-based tensor decomposition. The model uses a causal convolution on time features and a sigmoid-activated nonlinear fusion to reconstruct missing entries, while an SGD procedure learns parameters and a PSO-based mechanism automatically tunes hyperparameters. Empirical results on three real Victoria Harbour datasets show CLR achieves superior imputation accuracy (lower RMSE and MAE) and faster runtimes than several baselines, supporting more reliable environmental monitoring decisions. The approach advances imputation for WQD by jointly leveraging temporal causality, low-rank structure, and automated hyperparameter optimization, with potential extensions to exploit spatial structure.

Abstract

The monitoring of water quality is a crucial part of environmental protection, and a large number of monitors are widely deployed to monitor water quality. Due to unavoidable factors such as data acquisition breakdowns, sensors and communication failures, water quality monitoring data suffers from missing values over time, resulting in High-Dimensional and Sparse (HDS) Water Quality Data (WQD). The simple and rough filling of the missing values leads to inaccurate results and affects the implementation of relevant measures. Therefore, this paper proposes a Causal convolutional Low-rank Representation (CLR) model for imputing missing WQD to improve the completeness of the WQD, which employs a two-fold idea: a) applying causal convolutional operation to consider the temporal dependence of the low-rank representation, thus incorporating temporal information to improve the imputation accuracy; and b) implementing a hyperparameters adaptation scheme to automatically adjust the best hyperparameters during model training, thereby reducing the tedious manual adjustment of hyper-parameters. Experimental studies on three real-world water quality datasets demonstrate that the proposed CLR model is superior to some of the existing state-of-the-art imputation models in terms of imputation accuracy and time cost, as well as indicating that the proposed model provides more reliable decision support for environmental monitoring.

Figures (3)

• Figure 1: An illustration of water quality data constructed as an HDS tensor.
• Figure 2: An illustrative example of a tensor low-rank representation.
• Figure 3: An illustration of the causal convolutional transform for the time feature matrix with a 3$\times$1 convolution kernel size.