Beyond the Laplacian: Interpolated Spectral Augmentation for Graph Neural Networks
Ziyao Cui, Edric Tam
TL;DR
This work addresses the limitation of relying solely on Laplacian-based spectral features for GNN augmentation by introducing Interpolated Laplacian Embeddings (ILEs), derived from the two-parameter family M(t,s) = tD − sA. It provides a spectral-graph-theory interpretation of the embeddings via Rayleigh quotients and shows that varying (t,s) trades off community structure and core-periphery signals, potentially improving downstream node classification. Through extensive experiments on SBM simulations and real networks (with and without features, and with corrupted features), ILEs often outperform Laplacian embeddings, offering a practical guide for hyperparameter selection and emphasizing the value of a broader spectral toolkit. The work highlights the richness of non-Laplacian spectral representations for representation learning on graphs and paves the way for future extensions to directed, edge-featured, and dynamic graphs.
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.