Grouping-matrix based Graph Pooling with Adaptive Number of Clusters

TL;DR

This paper introduces GMPool, a differentiable graph pooling method that adaptively determines the number of clusters for each graph, improving hierarchical encoding in graph neural networks.

Contribution

GMPool is a novel pooling architecture that automatically learns the optimal number of clusters per graph using a grouping matrix and decomposition, unlike fixed-cluster methods.

Findings

Outperforms conventional graph pooling methods on molecular property prediction tasks.

Effectively adapts to varying cluster numbers across different graphs.

Demonstrates superior hierarchical encoding capabilities.

Abstract

Graph pooling is a crucial operation for encoding hierarchical structures within graphs. Most existing graph pooling approaches formulate the problem as a node clustering task which effectively captures the graph topology. Conventional methods ask users to specify an appropriate number of clusters as a hyperparameter, then assume that all input graphs share the same number of clusters. In inductive settings where the number of clusters can vary, however, the model should be able to represent this variation in its pooling layers in order to learn suitable clusters. Thus we propose GMPool, a novel differentiable graph pooling architecture that automatically determines the appropriate number of clusters based on the input data. The main intuition involves a grouping matrix defined as a quadratic form of the pooling operator, which induces use of binary classification probabilities of pairwise combinations of nodes. GMPool obtains the pooling operator by first computing the grouping matrix, then decomposing it. Extensive evaluations on molecular property prediction tasks demonstrate that our method outperforms conventional methods.