Beyond the Laplacian: Interpolated Spectral Augmentation for Graph Neural Networks

TL;DR

This paper introduces Interpolated Laplacian Embeddings (ILEs), a new spectral augmentation method for graph neural networks that enhances node features by leveraging alternative graph matrices, improving performance in feature-limited scenarios.

Contribution

The paper presents ILEs, a novel spectral augmentation technique derived from a family of graph matrices, expanding the spectral tools available for GNN feature augmentation.

Findings

ILEs improve GNN performance on real-world datasets.

Spectral embeddings from alternative matrices are effective for feature augmentation.

ILEs provide a practical and interpretable spectral augmentation method.

Abstract

Graph neural networks (GNNs) are fundamental tools in graph machine learning. The performance of GNNs relies crucially on the availability of informative node features, which can be limited or absent in real-life datasets and applications. A natural remedy is to augment the node features with embeddings computed from eigenvectors of the graph Laplacian matrix. While it is natural to default to Laplacian spectral embeddings, which capture meaningful graph connectivity information, we ask whether spectral embeddings from alternative graph matrices can also provide useful representations for learning. We introduce Interpolated Laplacian Embeddings (ILEs), which are derived from a simple yet expressive family of graph matrices. Using tools from spectral graph theory, we offer a straightforward interpretation of the structural information that ILEs capture. We demonstrate through simulations and experiments on real-world datasets that feature augmentation via ILEs can improve performance across commonly used GNN architectures. Our work offers a straightforward and practical approach that broadens the practitioner's spectral augmentation toolkit when node features are limited.