Cluster and Landmark Attributes Infused Graph Neural Networks for Link prediction

Minsang Kim, Seung Jun Baek

Keywords: Graph Neural Networks, Link prediction

Abstract: Learning positional information of nodes in a graph is important for link prediction tasks. We propose a simple representation of positional information using a set of representative nodes called landmarks. The position of a node is represented as a vector of its distances to the landmarks, where the landmarks are selected from the nodes with high degree centrality. We justify this selection strategy by analyzing well-known models of random graphs, and deriving closed-form bounds on the average path lengths involving landmarks. In a model for scale-free networks, we show that the distances to landmarks provide asymptotically accurate information on inter-node shortest distances. Our result is consistent with small-world phenomenon, i.e., a landmark can provide short paths between nodes as a hub. We apply theoretical insights to practical networks, and propose Cluster and Landmark Attributes-iNfused graph neural networks (CLAN). CLAN combines graph clustering and landmark selection, in which the graph is partitioned into densely connected clusters, and local node with the maximum degree is selected as landmarks. In addition, CLAN encodes the distances to landmarks using cluster-specific embedding in order to extract locality among the nodes in the common cluster. Experiments demonstrate that CLAN achieves superior performances and robustness over baseline methods on various datasets.

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TL;DR: We propose a simple representation of positional information using a set of representative nodes called landmarks, and show that the proposed method achieves superior link prediction performances on various datasets.