  Missing node attributes is a common problem in real-world graphs. Graph
neural networks have been demonstrated powerful in graph representation
learning, however, they rely heavily on the completeness of graph information.
Few of them consider the incomplete node attributes, which can bring great
damage to the performance in practice. In this paper, we propose an innovative
node representation learning framework, Wasserstein graph diffusion (WGD), to
mitigate the problem. Instead of feature imputation, our method directly learns
node representations from the missing-attribute graphs. Specifically, we extend
the message passing schema in general graph neural networks to a Wasserstein
space derived from the decomposition of attribute matrices. We test WGD in node
classification tasks under two settings: missing whole attributes on some nodes
and missing only partial attributes on all nodes. In addition, we find WGD is
suitable to recover missing values and adapt it to tackle matrix completion
problems with graphs of users and items. Experimental results on both tasks
demonstrate the superiority of our method.
