Persistence Homology for Link Prediction: An Interactive View

Abstract

Link prediction is an important learning task for graph-structured data. In this paper, we propose a novel topological approach to characterize interactions between two nodes. Our topological feature, based on the extended persistence homology, encodes rich structural information regarding the multi-hop paths connecting nodes. Based on this feature, we propose a graph neural network method that outperforms state-of-the-arts on different benchmarks. As another contribution, we propose a novel algorithm to more efficiently compute the extended persistent diagrams for graphs. This algorithm can be generally applied to accelerate many other topological methods for graph learning tasks.