Graph Neural Networks (GNNs) are powerful tools for graph classification. One important operation for GNNs is the downsampling or pooling that can learn effective embeddings from the node representations. In this paper, we propose a new hierarchical pooling operation, namely the Edge-Node Attention-based Differentiable Pooling (ENADPool), for GNNs to learn effective graph representations. Unlike the classical hierarchical pooling operation that is based on the unclear node assignment and simply computes the averaged feature over the nodes of each cluster, the proposed ENADPool not only employs a hard clustering strategy to assign each node into an unique cluster, but also compress the node features as well as their edge connectivity strengths into the resulting hierarchical structure based on the attention mechanism after each pooling step. As a result, the proposed ENADPool simultaneously identifies the importance of different nodes within each separated cluster and edges between corresponding clusters, that significantly addresses the shortcomings of the uniform edge-node based structure information aggregation arising in the classical hierarchical pooling operation. Moreover, to mitigate the over-smoothing problem arising in existing GNNs, we propose a Multi-distance GNN (MD-GNN) model associated with the proposed ENADPool operation, allowing the nodes to actively and directly receive the feature information from neighbors at different random walk steps. Experiments demonstrate the effectiveness of the MD-GNN associated with the proposed ENADPool.

翻译：图神经网络（GNN）是图分类的重要工具。其中下采样或池化操作能从节点表示中学习有效嵌入，是GNN的关键技术之一。本文提出一种新型层级池化操作——基于边-节点注意力的可微分池化（ENADPool），用于GNN以学习有效的图表示。与基于模糊节点分配、简单计算各簇节点平均特征的经典层级池化操作不同，所提ENADPool不仅采用硬聚类策略将每个节点分配至唯一簇，还在每次池化后基于注意力机制将节点特征及其边连接强度压缩至层级结构中。因此，ENADPool可同时识别分离簇内不同节点的重要性及对应簇间的边重要性，有效解决了经典层级池化中均匀化边-节点结构信息聚合的缺陷。此外，为缓解现有GNN中的过平滑问题，我们提出与ENADPool操作相关联的多距离图神经网络（MD-GNN）模型，使节点能够主动且直接地从不同随机游走步数的邻居接收特征信息。实验验证了所提MD-GNN结合ENADPool的有效性。