Graph Neural Networks achieve state-of-the-art performance on a plethora of
graph classification tasks, especially due to pooling operators, which
aggregate learned node embeddings hierarchically into a final graph
representation. However, they are not only questioned by recent work showing on
par performance with random pooling, but also ignore completely higher-order
connectivity patterns. To tackle this issue, we propose HoscPool, a
clustering-based graph pooling operator that captures higher-order information
hierarchically, leading to richer graph representations. In fact, we learn a
probabilistic cluster assignment matrix end-to-end by minimising relaxed
formulations of motif spectral clustering in our objective function, and we
then extend it to a pooling operator. We evaluate HoscPool on graph
classification tasks and its clustering component on graphs with ground-truth
community structure, achieving best performance. Lastly, we provide a deep
empirical analysis of pooling operators' inner functioning.

提出了 HoscPool，一种基于聚类的图池算子以及它的聚类组件，通过最小化松弛的基元谱聚类来学习概率群分配矩阵，从而丰富图形表示，并在图分类任务和地面真实社区结构图上取得了最佳表现。此外，对汇集算子的内部功能进行了深入的实证分析。