Wasserstein diffusion on graphs with missing attributes

Zhixian Chen, Tengfei Ma, Yangqiu Song, Yang Wang

Keywords: Wasserstein barycenter, graph learning, diffusion, missing features, matrix completion

Abstract:

Many real-world graphs are attributed graphs where nodes are associated with non-topological features. While attributes can be missing anywhere in an attributed graph, most of existing node representation learning approaches do not consider such incomplete information.
In this paper, we propose a general non-parametric framework to mitigate this problem. Starting from a decomposition of the attribute matrix, we transform node features into discrete distributions in a lower-dimensional space equipped with the Wasserstein metric. On this Wasserstein space, we propose Wasserstein graph diffusion to smooth the distributional representations of nodes with information from their local neighborhoods. This allows us to reduce the distortion caused by missing attributes and obtain integrated representations expressing information of both topology structures and attributes. We then pull the nodes back to the original space and produce corresponding point representations to facilitate various downstream tasks. To show the power of our representation method, we designed two algorithms based on it for node classification (with missing attributes) and matrix completion respectively, and demonstrate their effectiveness in experiments.

One-sentence Summary: We propose a new graph representation method based on optimal transport for graphs with missing attributes.

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