Edge Entropy as an Indicator of the Effectiveness of GNNs over CNNs for Node Classification

TL;DR

This paper introduces edge entropy as a metric to predict when GNNs will outperform CNNs in node classification tasks, based on the underlying graph structure's informativeness.

Contribution

The paper proposes edge entropy as a novel indicator for assessing the potential performance gains of GNNs over CNNs in node classification.

Findings

Lower edge entropy correlates with larger GNN performance gains.

Higher edge entropy predicts smaller improvements of GNNs over CNNs.

Edge entropy effectively indicates the usefulness of graph structure in GNNs.

Abstract

Graph neural networks (GNNs) extend convolutional neural networks (CNNs) to graph-based data. A question that arises is how much performance improvement does the underlying graph structure in the GNN provide over the CNN (that ignores this graph structure). To address this question, we introduce edge entropy and evaluate how good an indicator it is for possible performance improvement of GNNs over CNNs. Our results on node classification with synthetic and real datasets show that lower values of edge entropy predict larger expected performance gains of GNNs over CNNs, and, conversely, higher edge entropy leads to expected smaller improvement gains.