Edge-Based Graph Component Pooling

Graph-structured data naturally occurs in many research fields, such as chemistry and sociology. The relational information contained therein can be leveraged to statistically model graph properties through geometrical deep learning. Graph neural networks employ techniques, such as message-passing layers, to propagate local features through a graph. However, message-passing layers can be computationally expensive when dealing with large and sparse graphs. Graph pooling operators offer the possibility of removing or merging nodes in such graphs, thus lowering computational costs. However, pooling operators that remove nodes cause data loss, and pooling operators that merge nodes are often computationally expensive. We propose a pooling operator that merges nodes so as not to cause data loss but is also conceptually simple and computationally inexpensive. We empirically demonstrate that the proposed pooling operator performs statistically significantly better than edge pool on four popular benchmark datasets while reducing time complexity and the number of trainable parameters by 70.6% on average. Compared to another maximally powerful method named Graph Isomporhic Network, we show that we outperform them on two popular benchmark datasets while reducing the number of learnable parameters on average by 60.9%.