Robust Missing Value Imputation With Proximal Optimal Transport for Low-Quality IIoT Data

Accurate imputation of missing data is crucial in the Industrial Internet-of-Things (IIoT), where operations are often compromised by noisy samples from harsh environments. Traditional imputation methods struggle with such noise due to their black-box nature or lack of adaptability. To address this issue, we recast data imputation as a distribution alignment challenge, utilizing the flexibility of optimal transport (OT) to handle noisy samples. Specifically, we first introduce the Proximal Optimal Transport (POT) problem, where the transportation cost is obtained by the network simplex approach with a selective matching mechanism, which renders it capable of matching distributions with noisy samples. Subsequently, we propose the POT-I framework, where the objective is to minimize the transport cost of POT. The produced gradient is used to refine the imputation value, which achieves missing data imputation (MDI) while getting robustness to noisy samples. Experiments on real-world IIoT datasets demonstrate the superiority of POT-I over state-of-the-art imputation methods.