Graph Neural Networks (GNN) have been shown to work effectively for modeling graph structured data to solve tasks such as node classification, link prediction and graph classification. There has been some recent progress in defining the notion of pooling in graphs whereby the model tries to generate a graph level representation by downsampling and summarizing the information present in the nodes. Existing pooling methods either fail to effectively capture the graph substructure or do not easily scale to large graphs. In this work, we propose ASAP (Adaptive Structure Aware Pooling), a sparse and differentiable pooling method that addresses the limitations of previous graph pooling architectures. ASAP utilizes a novel self-attention network along with a modified GNN formulation to capture the importance of each node in a given graph. It also learns a sparse soft cluster assignment for nodes at each layer to effectively pool the subgraphs to form the pooled graph. Through extensive experiments on multiple datasets and theoretical analysis, we motivate our choice of the components used in ASAP. Our experimental results show that combining existing GNN architectures with ASAP leads to state-of-the-art results on multiple graph classification benchmarks. ASAP has an average improvement of 4\%, compared to current sparse hierarchical state-of-the-art method.

Advanced methods of applying deep learning to structured data such as graphs have been proposed in recent years. In particular, studies have focused on generalizing convolutional neural networks to graph data, which includes redefining the convolution and the downsampling (pooling) operations for graphs. The method of generalizing the convolution operation to graphs has been proven to improve performance and is widely used. However, the method of applying downsampling to graphs is still difficult to perform and has room for improvement. In this paper, we propose a graph pooling method based on self-attention. Self-attention using graph convolution allows our pooling method to consider both node features and graph topology. To ensure a fair comparison, the same training procedures and model architectures were used for the existing pooling methods and our method. The experimental results demonstrate that our method achieves superior graph classification performance on the benchmark datasets using a reasonable number of parameters.