A Non-Negative Factorization approach to node pooling in Graph Convolutional Neural Networks

TL;DR

This paper introduces a graph pooling method based on Non-Negative Matrix Factorization that adaptively coarsens graphs, leading to improved classification performance in graph neural networks.

Contribution

It proposes a novel NMF-based pooling mechanism for GCNs that enhances graph coarsening and improves predictive accuracy.

Findings

Significant performance improvements on graph classification benchmarks.

Effective adaptive pooling based on node similarity and community detection.

Enhanced graph coarsening preserves important structural information.

Abstract

The paper discusses a pooling mechanism to induce subsampling in graph structured data and introduces it as a component of a graph convolutional neural network. The pooling mechanism builds on the Non-Negative Matrix Factorization (NMF) of a matrix representing node adjacency and node similarity as adaptively obtained through the vertices embedding learned by the model. Such mechanism is applied to obtain an incrementally coarser graph where nodes are adaptively pooled into communities based on the outcomes of the non-negative factorization. The empirical analysis on graph classification benchmarks shows how such coarsening process yields significant improvements in the predictive performance of the model with respect to its non-pooled counterpart.