Graph Classification Gaussian Processes via Hodgelet Spectral Features

2024-10-14

arXiv.org

AI Summary

Existing graph classification methods—including graph neural networks, graph kernels, and conventional Gaussian processes—primarily model only vertex features while neglecting edge-structural information, leading to insufficient representation of graph complexity. To address this limitation, we propose HodgeGP: the first Gaussian process framework for graph classification that incorporates Hodge decomposition. HodgeGP extracts multi-order spectral signals—termed *Hodgelet features*—that jointly encode vertex and edge structures via Hodge decomposition, embeds graphs into Euclidean space, and seamlessly integrates with classical kernel functions. By unifying point-line (vertex-edge) structural modeling, HodgeGP breaks away from the dominant vertex-centric paradigm. Extensive experiments on multiple standard graph benchmarks demonstrate significant improvements in classification accuracy, particularly on edge-sensitive tasks. These results validate the expressive power and generalizability of Hodgelet features, establishing HodgeGP as a principled and effective approach for structure-aware graph learning.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Bridging structured and unstructured data

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.

Problem

• Graph Classification
• Graph Neural Networks
• Gaussian Processes

Innovation

• Hodgelet Spectral Features
• Gaussian Processes
• Graph Classification