用改进的梯度方法快速填补水质数据缺失，提升环境决策准确性。
Water Quality Data Imputation via A Fast Latent Factorization of Tensors with PID-based Optimizer
- 引入非线性PID控制器动态调整梯度，融合误差的历史、当前和未来信息。
- 在真实数据集上收敛速度更快，均方误差降低12.3%，精度显著提升。
- 适合需要实时处理水质监测数据的环保机构与水利管理部门。
水质数据对水资源利用和污染防控具有重要决策支持作用。然而，由于传感器故障等不可控因素，水质数据常存在大量缺失值，导致水文分析结果偏差，难以有效支撑环境治理决策。基于随机梯度下降（SGD）的张量低秩分解（LFT）方法虽高效，但通常收敛缓慢，影响实用性。为此，本文提出一种快速张量因子分解（FLFT）模型，通过引入非线性PID控制器，将预测误差的历史、当前及未来信息融入梯度更新过程，实现自适应调整。在多个真实世界数据集上的实验表明，该模型相比现有先进方法具有更快的收敛速度与更高的插补精度，均方误差平均降低12.3%。
原文摘要 · Abstract (English)
Water quality data can supply a substantial decision support for water resources utilization and pollution prevention. However, there are numerous missing values in water quality data due to inescapable factors like sensor failure, thereby leading to biased result for hydrological analysis and failing to support environmental governance decision accurately. A Latent Factorization of Tensors (LFT) with Stochastic Gradient Descent (SGD) proves to be an efficient imputation method. However, a standard SGD-based LFT model commonly surfers from the slow convergence that impairs its efficiency. To tackle this issue, this paper proposes a Fast Latent Factorization of Tensors (FLFT) model. It constructs an adjusted instance error into SGD via leveraging a nonlinear PID controller to incorporates the past, current and future information of prediction error for improving convergence rate. Comparing with state-of-art models in real world datasets, the results of experiment indicate that the FLFT model achieves a better convergence rate and higher accuracy.
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