DIPool: Degree-Induced Pooling for Hierarchical Graph Representation Learning.

Graph Neural Networks have been popularly investigated and achieved promising performance in node-wise and graph-level tasks, like node classification and graph classification. For graph classification, correctly defining pooling operations to coarsen an input graph for distilling hierarchical knowledge from node representations is demanded. Some works have devised pooling strategies to summarize a graph by evaluating and gathering the ranked top-k representative nodes. Yet there is few literature to explicitly consider the node's degree-specific structure information in pooling procedure. One intuition is the larger the node's degree is, the more important it probably is in the entire graph. In this work, we propose a novel Degree-Induced Pooling (DIPool), which can be integrated into various graph neural network architectures. Specifically, the DIPool layer devises two approaches for explicitly incorporating the characteristics and degree-specific structures of nodes into a unified criterion to evaluate the importance of the nodes within an input graph. This setting permits to retain more representative nodes to generate the newly pooled graph. Experimental results on a collection of public benchmarks have demonstrated the effectiveness of the proposed DIPool operator. Especially, DIPool achieves relative improvements of 3.69% on NCI1 and 3.24% on NCI109 compared with the best baseline ASAP.