BN-Pool: a Bayesian Nonparametric Approach to Graph Pooling

2025-01-16

AI Summary

Predefined numbers of supernodes in graph pooling often cause structural distortion or excessive simplification. To address this, we propose BN-Pool—the first differentiable graph pooling method based on Bayesian nonparametric clustering. It employs the Chinese Restaurant Process (CRP) prior to enable unbounded, adaptive learning of the number of supernodes, eliminating the need for manual specification of pooling ratios. BN-Pool jointly optimizes cluster structure and node representations in a task-driven manner by integrating supervised classification loss with graph topology reconstruction loss. Extensive experiments on multiple benchmark datasets demonstrate that BN-Pool consistently outperforms state-of-the-art pooling methods, achieving superior classification accuracy and greater flexibility in coarse-grained graph structure generation. Notably, it is the first work to systematically introduce Bayesian nonparametric modeling into graph coarsening, establishing a principled framework for data-adaptive hierarchical graph representation learning.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

We introduce BN-Pool, the first clustering-based pooling method for Graph Neural Networks (GNNs) that adaptively determines the number of supernodes in a coarsened graph. By leveraging a Bayesian non-parametric framework, BN-Pool employs a generative model capable of partitioning graph nodes into an unbounded number of clusters. During training, we learn the node-to-cluster assignments by combining the supervised loss of the downstream task with an unsupervised auxiliary term, which encourages the reconstruction of the original graph topology while penalizing unnecessary proliferation of clusters. This adaptive strategy allows BN-Pool to automatically discover an optimal coarsening level, offering enhanced flexibility and removing the need to specify sensitive pooling ratios. We show that BN-Pool achieves superior performance across diverse benchmarks.

Problem

• Graph Neural Networks
• Super Node Adjustment
• Efficient Graph Processing

Innovation

• BN-Pool
• Bayesian Techniques
• Adaptive Graph Simplification