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。

图神经网络的高阶聚类和池化

Higher-order Clustering and Pooling for Graph Neural Networks

Networks are a fundamental tool for understanding and modeling complex
systems in physics, biology, neuroscience, engineering, and social science.
Many networks are known to exhibit rich, lower-order connectivity patterns that
can be captured at the level of individual nodes and edges. However,
higher-order organization of complex networks---at the level of small network
subgraphs---remains largely unknown. Here we develop a generalized framework
for clustering networks based on higher-order connectivity patterns. This
framework provides mathematical guarantees on the optimality of obtained
clusters and scales to networks with billions of edges. The framework reveals
higher-order organization in a number of networks including information
propagation units in neuronal networks and hub structure in transportation
networks. Results show that networks exhibit rich higher-order organizational
structures that are exposed by clustering based on higher-order connectivity
patterns.

基于高阶连接模式的聚类可以揭示网络的高阶组织结构，此框架对于大规模网络的优化性能具有数学保证。