Maximal Independent Sets for Pooling in Graph Neural Networks

TL;DR

This paper introduces three novel graph pooling methods based on maximal independent sets, addressing key limitations of existing techniques by maintaining connectivity and improving decimation ratios in graph neural networks.

Contribution

The paper proposes new graph pooling methods utilizing maximal independent sets, overcoming issues like disconnection and low decimation ratios present in prior approaches.

Findings

Maximal independent set-based pooling preserves graph connectivity.

The methods achieve higher decimation ratios than existing approaches.

Experimental results validate the effectiveness of the proposed pooling techniques.

Abstract

Convolutional Neural Networks (CNNs) have enabled major advances in image classification through convolution and pooling. In particular, image pooling transforms a connected discrete lattice into a reduced lattice with the same connectivity and allows reduction functions to consider all pixels in an image. However, there is no pooling that satisfies these properties for graphs. In fact, traditional graph pooling methods suffer from at least one of the following drawbacks: Graph disconnection or overconnection, low decimation ratio, and deletion of large parts of graphs. In this paper, we present three pooling methods based on the notion of maximal independent sets that avoid these pitfalls. Our experimental results confirm the relevance of maximal independent set constraints for graph pooling.