Higher-order Clustering and Pooling for Graph Neural Networks

TL;DR

This paper introduces HoscPool, a novel clustering-based pooling operator for graph neural networks that captures higher-order connectivity patterns, leading to improved graph classification performance and richer representations.

Contribution

It proposes a new pooling method that learns probabilistic cluster assignments to incorporate higher-order information in GNNs, addressing limitations of existing pooling techniques.

Findings

HoscPool outperforms existing pooling methods on graph classification tasks.

The clustering component accurately identifies ground-truth community structures.

Empirical analysis reveals insights into pooling operators' inner workings.

Abstract

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.