The challenge of accurately classifying complex networks is driving innovation in topological data analysis, and researchers are currently seeking ways to best capture the underlying structure of graphs. Xinyang Chen from Harbin Institute of Technology and the University of Lille, along with Amaël Broustet and Guoting Chen from the University of Great Bay and the University of Lille, introduces a new method to extract meaningful features from graph data and significantly improve classification performance. Their work introduces frequent subgraph filtering, a technique that identifies repeated patterns within a dataset to create more stable and informative topological features than traditional approaches. By bridging frequent subgraph mining with persistent homology, the team develops both a machine learning model and a framework for powering graph neural networks, achieving significant performance improvements across several benchmark datasets and providing a powerful new approach to topology-aware feature extraction.
Persistent homology improves learning of graph representations
This work focuses on topological data analysis (TDA), specifically enhancing the learning and classification of graph representations by integrating persistent homology. This approach aims to capture the underlying shape of a graph and reveal important structural information that is often missed by traditional graph neural networks (GNNs). The team will explore ways to incorporate topological features into GNN architectures to improve their ability to understand complex relationships within graphs. Persistent homology identifies and tracks topological features such as connected components and loops as scale parameters change, resulting in a persistent diagram that summarizes these features.
This work also frequently investigates subgraph mining and graph kernels as techniques for extracting meaningful features and measuring graph similarity. Simple complexes representing higher-dimensional structures are often used in combination with persistent homology to provide a more comprehensive analysis. Researchers are exploring ways to combine persistent homology with GNNs, such as using persistence diagrams as input features or designing GNN layers that explicitly incorporate topological information. Methods such as Persistence Landscapes/Images convert persistence diagrams into a format suitable for machine learning models. Additionally, techniques such as Graph2Vec and Weisfeiler-Lehman Graph Kernels provide alternative approaches to graph representation.
Cluster-guided contrastive learning leverages cluster information to further refine graph classification. This research utilizes datasets such as Open Graph Benchmark (OGB) and applies TDA to various fields such as functional brain connectivity analysis, geographic information science, and quantum chemistry. Current challenges include the scalability of TDA for large graphs, interpretability of topological features, and handling of dynamic graphs. Future research will aim to address these limitations, improve the visualization of persistent homology results, and ultimately provide more robust and informative ways to represent graphs for machine learning tasks.
Frequent subgraph filtering to maintain homology
In this study, we introduce Frequent Subgraph Filtration (FSF), a novel technique that improves persistent homology for extracting topological features from graph data. Unlike existing methods that rely on simple edge weights or vertex degrees, FSF mines frequent subgraphs across datasets and builds filters based on isomorphic mappings to these patterns, capturing recurrent structural information and global topology. The researchers rigorously analyzed the stability and information richness of the obtained frequency-based persistent homology (FPH) features and confirmed the theoretical properties of FSF. In this study, two classification approaches are introduced. One is FPH-ML, which is a traditional machine learning model that leverages the capabilities of FPH, and the other is FPH-GNN, which integrates FPH into a graph neural network for topology-aware representation learning.
Experiments on benchmark datasets demonstrate that FPH-ML achieves competitive or superior accuracy compared to kernel-based and order-based filtering techniques. Integrating FPH into graph neural networks significantly improves graph classification accuracy with relative performance improvements of 0.4 to 21 percent and up to 8.2 percentage points compared to GCN and GIN backbones. This study bridges the frequently performed subgraph mining and topological data analysis and provides a new perspective on feature extraction and graph representation.
Frequent use of subgraphs improves graph classification accuracy
Scientists have developed Frequency Subgraph Filtration (FSF) to enhance persistent homology and improve the accuracy of graph classification. This frequency-driven approach, unlike traditional filtering, integrates frequently occurring subgraph patterns and captures recurring structural information and dataset-level topology. Theoretical analysis confirms the properties of FSF, such as a bounded persistent homology dimension and demonstrated monotonicity and isomorphic invariance. The FPH-ML model is based on frequency-based persistent homology and achieves competitive or superior accuracy compared to kernel-based and order-based filtering methods.
Integrating FPH into a graph neural network (FPH-GNN) achieved relative performance improvements of 0.4 to 21 percent across benchmark datasets, and up to 8.2 percentage points compared to GCN and GIN backbones, demonstrating significant advances in topology-aware representation learning. The team measured performance improvements using both the FPH-ML model and the FPH-GNN hybrid framework, establishing a new perspective on topology-aware feature extraction. This approach exploits repeating patterns in graphs to create more detailed and stable analyzes and overcomes the limitations of existing methods that rely on limited structural inspection. The researchers took advantage of this new topological data to develop two models: a machine learning model and a hybrid framework integrated with graph neural networks. Machine learning models achieve similar or better accuracy than existing methods based on kernel or order-based filtering.
Incorporating this approach into graph neural networks yields performance improvements of up to 8.2 percentage points compared to standard architectures, ranging from 0.4 to 21 percent across several benchmark datasets. The authors acknowledge that the computational cost of identifying frequently occurring subgraphs remains a limitation, especially for very large graphs, and suggest future optimizations. They also consider applying the method to other data types and suggest the possibility of extending its impact to different scientific fields.
