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Label Propagation (LPA) and Graph Convolutional Neural Networks (GCN) areboth message passing algorithms on graphs. Both solve the task of nodeclassification but LPA propagates node label information across the edges ofthe graph, while GCN propagates and transforms node feature information.However, while conceptually similar, theoretical relation between LPA and GCNhas not yet been investigated. Here we study the relationship between LPA andGCN in terms of two aspects: (1) feature/label smoothing where we analyze howthe feature/label of one node is spread over its neighbors; And, (2)feature/label influence of how much the initial feature/label of one nodeinfluences the final feature/label of another node. Based on our theoreticalanalysis, we propose an end-to-end model that unifies GCN and LPA for nodeclassification. In our unified model, edge weights are learnable, and the LPAserves as regularization to assist the GCN in learning proper edge weights thatlead to improved classification performance. Our model can also be seen aslearning attention weights based on node labels, which is more task-orientedthan existing feature-based attention models. In a number of experiments onreal-world graphs, our model shows superiority over state-of-the-art GCN-basedmethods in terms of node classification accuracy.

Unifying Graph Convolutional Neural Networks and Label Propagation