  Graph neural networks (GNN) have been proven to be mature enough for handling
graph-structured data on node-level graph representation learning tasks.
However, the graph pooling technique for learning expressive graph-level
representation is critical yet still challenging. Existing pooling methods
either struggle to capture the local substructure or fail to effectively
utilize high-order dependency, thus diminishing the expression capability. In
this paper we propose HAP, a hierarchical graph-level representation learning
framework, which is adaptively sensitive to graph structures, i.e., HAP
clusters local substructures incorporating with high-order dependencies. HAP
utilizes a novel cross-level attention mechanism MOA to naturally focus more on
close neighborhood while effectively capture higher-order dependency that may
contain crucial information. It also learns a global graph content GCont that
extracts the graph pattern properties to make the pre- and post-coarsening
graph content maintain stable, thus providing global guidance in graph
coarsening. This novel innovation also facilitates generalization across graphs
with the same form of features. Extensive experiments on fourteen datasets show
that HAP significantly outperforms twelve popular graph pooling methods on
graph classification task with an maximum accuracy improvement of 22.79%, and
exceeds the performance of state-of-the-art graph matching and graph similarity
learning algorithms by over 3.5% and 16.7%.
