Grouping-matrix based Graph Pooling with Adaptive Number of Clusters

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.

10 pages, 3 figures

References in corpus (15)

• Semi-Supervised Classification with Graph Convolutional Networks
• Inductive Representation Learning on Large Graphs
• Neural Message Passing for Quantum Chemistry
• Spectral Networks and Locally Connected Networks on Graphs
• Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering
• Convolutional Networks on Graphs for Learning Molecular Fingerprints
• Hierarchical Graph Representation Learning with Differentiable Pooling
• Self-Attention Graph Pooling
• Analyzing Learned Molecular Representations for Property Prediction
• Learning Multimodal Graph-to-Graph Translation for Molecular Optimization
• Robust Differentiable SVD
• Training Deep Networks with Structured Layers by Matrix Backpropagation
• A Hierarchical Singular Value Decomposition Algorithm for Low Rank Matrices
• Backpropagation-Friendly Eigendecomposition
• Fast Differentiable Matrix Square Root

Cited by in corpus (2)

• Predicting Long-term Dynamics of Complex Networks via Identifying Skeleton in Hyperbolic Space
• Co-attention Graph Pooling for Efficient Pairwise Graph Interaction Learning