Title: Frequent Subgraph-Based Persistent Homology for Graph Classification
Primary area: learning on graphs and other geometries & topologies
Keywords: Frequent subgraph mining; Persistent homology; Filtration construction; Graph Classification

Abstract: Persistent homology (PH) has recently emerged as a powerful tool for extracting topological features. 
Integrating PH into both machine learning and deep learning models enhances their topology-awareness and interpretability.
However, most PH methods on graphs rely on a limited set of filtrations (e.g., degree- or weight-based), which overlook richer features such as recurring information across the dataset, thereby restricting their expressive power. In this work, we propose a novel filtration on graphs, called Frequent Subgraph Filtration (FSF), which is derived from frequent subgraphs and produces stable and information-rich Frequency-based Persistent Homology (FPH) features. We explore the theoretical properties of FSF and provide proofs and experimental validation of them. Beyond persistent homology itself, we further introduce two approaches for graph classification: (i) an FPH-based machine learning model (FPH-ML), and (ii) a hybrid framework integrating FPH with graph neural networks (FPH-GNNs) to enhance topology-aware graph representation learning. Our proposed frameworks show the potential of bridging frequent subgraph mining and topological data analysis, offering a new perspective on topology-aware feature extraction and graph representation learning.
Experimental results show that FPH-ML achieves competitive or superior accuracy compared to kernel-based and degree-based filtration methods. When injected into GNNs, FPH delivers relative gains of ~0.4–21\% (up to +8.2 pts) over their GCN/GIN backbones across benchmarks.

TL;DR: This paper proposes a novel filtration on graphs to compute persistent homology, derived from frequent subgraphs, termed Frequent Subgraph Filtration (FSF).