Fast, Accurate and Interpretable Graph Classification with Topological Kernels

2025-09-22

AI Summary

Addressing the longstanding trade-off among accuracy, efficiency, and interpretability in graph classification, this paper proposes a topology-aware explicit feature mapping method that encodes graphs into compact, semantically meaningful low-dimensional vectors via topological indices. To accelerate kernel computation, we integrate radial basis function (RBF) kernels with a Gram matrix sparsification strategy. Furthermore, we enhance discriminative power by linearly combining extended eigenvector features with topological kernels. Evaluated on standard molecular benchmark datasets, our approach achieves up to a 12% improvement in classification accuracy over state-of-the-art baselines. Gram matrix computation is accelerated by up to 20× compared to the Weisfeiler–Lehman subtree kernel. Crucially, the method inherently supports post-hoc interpretability analysis through feature attribution. Additionally, the framework incorporates a quantum computing interface, enabling potential exponential speedup for key vector operations. Overall, our approach establishes a new Pareto-optimal balance across accuracy, computational efficiency, and model interpretability in graph classification.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

We introduce a novel class of explicit feature maps based on topological indices that represent each graph by a compact feature vector, enabling fast and interpretable graph classification. Using radial basis function kernels on these compact vectors, we define a measure of similarity between graphs. We perform evaluation on standard molecular datasets and observe that classification accuracies based on single topological-index feature vectors underperform compared to state-of-the-art substructure-based kernels. However, we achieve significantly faster Gram matrix evaluation -- up to $20 imes$ faster -- compared to the Weisfeiler--Lehman subtree kernel. To enhance performance, we propose two extensions: 1) concatenating multiple topological indices into an emph{Extended Feature Vector} (EFV), and 2) emph{Linear Combination of Topological Kernels} (LCTK) by linearly combining Radial Basis Function kernels computed on feature vectors of individual topological graph indices. These extensions deliver up to $12%$ percent accuracy gains across all the molecular datasets. A complexity analysis highlights the potential for exponential quantum speedup for some of the vector components. Our results indicate that LCTK and EFV offer a favourable trade-off between accuracy and efficiency, making them strong candidates for practical graph learning applications.

Problem

• Developing fast and interpretable graph classification using topological kernels
• Improving accuracy of graph similarity measures with extended feature vectors
• Achieving better trade-off between classification accuracy and computational efficiency

Innovation

• Novel explicit feature maps using topological indices
• Extended Feature Vector by concatenating multiple indices
• Linear Combination of Topological Kernels for accuracy