  Graph neural networks (GNNs) have revolutionized the field of machine
learning on non-Euclidean data such as graphs and networks. GNNs effectively
implement node representation learning through neighborhood aggregation and
achieve impressive results in many graph-related tasks. However, most
neighborhood aggregation approaches are summation-based, which can be
problematic as they may not be sufficiently expressive to encode informative
graph structures. Furthermore, though the graph pooling module is also of vital
importance for graph learning, especially for the task of graph classification,
research on graph down-sampling mechanisms is rather limited.
  To address the above challenges, we propose a concatenation-based graph
convolution mechanism that injectively updates node representations to maximize
the discriminative power in distinguishing non-isomorphic subgraphs. In
addition, we design a novel graph pooling module, called WL-SortPool, to learn
important subgraph patterns in a deep-learning manner. WL-SortPool layer-wise
sorts node representations (i.e. continuous WL colors) to separately learn the
relative importance of subtrees with different depths for the purpose of
classification, thus better characterizing the complex graph topology and rich
information encoded in the graph. We propose a novel Subgraph Pattern GNN
(SPGNN) architecture that incorporates these enhancements. We test the proposed
SPGNN architecture on many graph classification benchmarks. Experimental
results show that our method can achieve highly competitive results with
state-of-the-art graph kernels and other GNN approaches.
