Wasserstein Graph Neural Networks for Graphs With Missing Attributes

Missing node attributes pose a common problem in real-world graphs, impacting the performance of graph neural networks’ representation learning. Existing GNNs often struggle to effectively leverage incomplete attribute information, as they are not specifically designed for graphs with missing attributes. To address this issue, we propose a novel node representation learning framework called Wasserstein Graph Neural Network (WGNN). Our approach aims to maximize the utility of limited observed attribute information and account for uncertainty caused by missing values. We achieve this by representing nodes as low-dimensional distributions obtained through attribute matrix decomposition. Additionally, we enhance representation expressiveness by introducing a unique message-passing schema that aggregates distributional information from neighboring nodes in the Wasserstein space. We evaluate the performance of WGNN in node classification tasks using both synthetic and real-world datasets under two missing-attribute scenarios. Moreover, we demonstrate the applicability of WGNN in recovering missing values and tackling matrix completion problems, specifically in graphs involving users and items. Experimental results on both tasks convincingly demonstrate the superiority of our proposed method.