SPOT-I: Similarity Preserved Optimal Transport for Industrial IoT Data Imputation

Missing data imputation is a critical aspect of the Industrial Internet-of-Things (IIoT), which is uniquely challenged by local relationships within data due to different operational contexts and phases. Current imputation methods struggle to accommodate local relationships due to their black-box nature or limited capacity. To bridge this gap, we approach data imputation as a distribution alignment problem and leverage optimal transport to instantiate it for enhanced capacity. Specifically, we first introduce the similarity preserved optimal transport (SPOT) problem, with a conditional gradient solution to compute the transport cost. Subsequently, we propose the SPOT for imputation (SPOT-I) framework. It minimizes the transport cost of SPOT for distribution alignment and uses the gradient to update imputations, which maintains local similarity and refines imputation due to the characteristics of SPOT. Experiments on IIoT datasets showcase the superiority of SPOT-I over state-of-the-art imputation methods.