Graph Classification Gaussian Processes via Hodgelet Spectral Features
Mathieu Alain, So Takao, Xiaowen Dong, Bastian Rieck, Emmanuel Noutahi
TL;DR
The paper addresses graph classification with both vertex and edge features by mapping spatial graph data to Euclidean spectral features through graph wavelets on the discrete Hodge Laplacians. A Gaussian process classifier is then applied with an additive Hodgelet kernel that separately models exact, co-exact, and harmonic components, enabling multi-resolution, isomorphism-invariant representations. Empirically, the Hodge decomposition improves performance over the baseline wavelet-GP on several benchmarks and enables effective edge-feature usage, with vector-field experiments showing strong gains, especially at finer mesh resolutions. The approach is data-efficient, uncertainty-aware, and naturally extendable to higher-order networks and regression tasks.
Abstract
The problem of classifying graphs is ubiquitous in machine learning. While it is standard to apply graph neural networks or graph kernel methods, Gaussian processes can be employed by transforming spatial features from the graph domain into spectral features in the Euclidean domain, and using them as the input points of classical kernels. However, this approach currently only takes into account features on vertices, whereas some graph datasets also support features on edges. In this work, we present a Gaussian process-based classification algorithm that can leverage one or both vertex and edges features. Furthermore, we take advantage of the Hodge decomposition to better capture the intricate richness of vertex and edge features, which can be beneficial on diverse tasks.