  Pooling operations have shown to be effective on computer vision and natural
language processing tasks. One challenge of performing pooling operations on
graph data is the lack of locality that is not well-defined on graphs. Previous
studies used global ranking methods to sample some of the important nodes, but
most of them are not able to incorporate graph topology. In this work, we
propose the topology-aware pooling (TAP) layer that explicitly considers graph
topology. Our TAP layer is a two-stage voting process that selects more
important nodes in a graph. It first performs local voting to generate scores
for each node by attending each node to its neighboring nodes. The scores are
generated locally such that topology information is explicitly considered. In
addition, graph topology is incorporated in global voting to compute the
importance score of each node globally in the entire graph. Altogether, the
final ranking score for each node is computed by combining its local and global
voting scores. To encourage better graph connectivity in the sampled graph, we
propose to add a graph connectivity term to the computation of ranking scores.
Results on graph classification tasks demonstrate that our methods achieve
consistently better performance than previous methods.
