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.

本文提出了一种名为 Edge-Node Attention-based Differentiable Pooling (ENADPool) 的新层次池化操作，用于学习有效的图表示，同时还提出了与 ENADPool 操作相关的多距离 GNN (MD-GNN) 模型，以解决传统层次池化操作中存在的问题。