Frequent subgraph-based persistent homology for graph classification
Xinyang Chen, Amaël Broustet, Guanyuan Zeng, Cheng He, Guoting Chen
TL;DR
This work introduces Frequent Subgraph Filtration (FSF), a dataset-driven topological filtration built from frequent subgraph patterns, to enrich persistent homology features for graph classification. It proves key properties such as a PH-dimension bound tied to the pattern size, monotonic filtration, and isomorphism invariance, and integrates FSF into two classification pipelines: FPH-ML and FPH-GNN. Empirical results show FSF-based methods outperform kernel-based, PH-based, and many GNN baselines on multiple benchmarks, with robust performance under perturbations and scalable options via budget-controlled FSM. By bridging frequent subgraph mining (FSM) and topological data analysis (TDA), the approach yields global, high-order topology aware representations that enhance both traditional ML and deep learning on graphs, albeit with recognized computational trade-offs that can be mitigated with approximate or budgeted FSM.
Abstract
Persistent homology (PH) has recently emerged as a powerful tool for extracting topological features. Integrating PH into machine learning and deep learning models enhances topology awareness and interpretability. However, most PH methods on graphs rely on a limited set of filtrations, such as degree-based or weight-based filtrations, which overlook richer features like recurring information across the dataset and thus restrict expressive power. In this work, we propose a novel graph filtration called Frequent Subgraph Filtration (FSF), which is derived from frequent subgraphs and produces stable and information-rich frequency-based persistent homology (FPH) features. We study the theoretical properties of FSF and provide both proofs and experimental validation. Beyond persistent homology itself, we introduce two approaches for graph classification: an FPH-based machine learning model (FPH-ML) and a hybrid framework that integrates FPH with graph neural networks (FPH-GNNs) to enhance topology-aware graph representation learning. Our frameworks bridge frequent subgraph mining and topological data analysis, offering a new perspective on topology-aware feature extraction. Experimental results show that FPH-ML achieves competitive or superior accuracy compared with kernel-based and degree-based filtration methods. When integrated into graph neural networks, FPH yields relative performance gains ranging from 0.4 to 21 percent, with improvements of up to 8.2 percentage points over GCN and GIN backbones across benchmarks.