# Water Quality Data Imputation via A Fast Latent Factorization of Tensors with PID-based Optimizer

arXiv: https://arxiv.org/abs/2503.06997 · HTML: https://mlsanity.com/paper/2503.06997/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 60 references that are in the map.
- First posted on arXiv 10 Mar 2025.

## Builds on (most cited first, 4 of 4)

- [Accelerating Minibatch Stochastic Gradient Descent using Typicality Sampling](https://mlsanity.com/paper/1903.04192/) (2019)
- [An ADRC-Incorporated Stochastic Gradient Descent Algorithm for Latent Factor Analysis](https://mlsanity.com/paper/2401.07012/) (2024)
- [Predicting Urban Water Quality with Ubiquitous Data](https://mlsanity.com/paper/1610.09462/) (2016)
- [STSyn: Speeding Up Local SGD with Straggler-Tolerant Synchronization](https://mlsanity.com/paper/2210.03521/) (2022)

## Abstract (arXiv)

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.