Topology-aware Machine Learning Enables Better Graph Classification with 0.4 Gain

The challenge of accurately classifying complex networks drives innovation in topological data analysis, and researchers are now exploring how to best capture a graph’s underlying structure. Xinyang Chen from Harbin Institute of Technology and Université de Lille, alongside Amaël Broustet and Guoting Chen from Great Bay University and Université de Lille, present a new method for extracting meaningful features from graph data, significantly improving classification performance. Their work introduces Frequent Subgraph Filtration, a technique that identifies recurring 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 to enhance graph neural networks, achieving substantial performance gains across several benchmark datasets and offering a powerful new approach to topology-aware feature extraction.

Persistent Homology Improves Graph Representation Learning

The research focuses on enhancing graph representation learning and classification by integrating Topological Data Analysis (TDA), specifically Persistent Homology. This approach aims to capture the underlying shape of a graph, revealing crucial structural information often missed by traditional graph neural networks (GNNs). The team explores methods to incorporate topological features into GNN architectures, improving their ability to understand complex relationships within graphs. Persistent homology identifies and tracks topological features, such as connected components and loops, as a scale parameter changes, resulting in a persistence diagram that summarizes these features.

The study also investigates frequent subgraph mining and graph kernels as techniques for extracting meaningful features and measuring graph similarity. Simplicial complexes, which represent higher-dimensional structures, are often used in conjunction with persistent homology to provide a more comprehensive analysis. Researchers are exploring ways to combine persistent homology with GNNs, including using persistence diagrams as input features or designing GNN layers that explicitly incorporate topological information. Methods like Persistence Landscapes/Images transform persistence diagrams into formats suitable for machine learning models, while techniques like Graph2Vec and Weisfeiler-Lehman Graph Kernels offer alternative approaches to graph representation.

Cluster-Guided Contrastive Learning further refines graph classification by leveraging clustering information. The research utilizes datasets like the Open Graph Benchmark (OGB) and applies TDA to diverse fields such as brain functional connectivity analysis, geographical information science, and quantum chemistry. Current challenges include the scalability of TDA for large graphs, the interpretability of topological features, and handling dynamic graphs. Future work aims to address these limitations and improve the visualization of persistent homology results, ultimately providing a more robust and informative way to represent graphs for machine learning tasks.

Frequent Subgraph Filtration for Persistent Homology

This study introduces Frequent Subgraph Filtration (FSF), a novel technique to improve 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 a dataset and constructs a filtration based on isomorphic mapping to these patterns, capturing recurring structural information and global topology. Researchers rigorously analyzed the stability and information richness of the resulting Frequency-based Persistent Homology (FPH) features, confirming the theoretical properties of FSF. The work introduces two classification approaches: FPH-ML, a traditional machine learning model utilizing FPH features, and FPH-GNNs, which integrates FPH into graph neural networks for topology-aware representation learning.

Experiments on benchmark datasets demonstrate that FPH-ML achieves competitive or superior accuracy compared to kernel-based and degree-based filtration techniques. Integrating FPH into graph neural networks 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, significantly enhancing graph classification accuracy. This work bridges frequent subgraph mining and topological data analysis, offering a new perspective on feature extraction and graph representation.

Frequent Subgraphs Enhance Graph Classification Accuracy

Scientists developed Frequent Subgraph Filtration (FSF) to enhance persistent homology and improve graph classification accuracy. This frequency-driven approach integrates frequent subgraph patterns, capturing recurring structural information and dataset-level topology, unlike traditional filtrations. Theoretical analysis confirms the properties of FSF, including a bounded persistence homology dimension and demonstrated monotonicity and isomorphism invariance. The FPH-ML model, based on Frequency-based Persistent Homology, achieves competitive or superior accuracy compared to kernel-based and degree-based filtration methods.

Integrating FPH into graph neural networks (FPH-GNNs) delivers relative performance gains ranging from 0.4 to 21 percent across benchmark datasets, with improvements of up to 8.2 percentage points over GCN and GIN backbones, demonstrating a significant advancement in topology-aware representation learning. The team measured performance gains using both the FPH-ML model and the FPH-GNN hybrid framework, establishing a new perspective on topology-aware feature extraction. This approach leverages recurring patterns within the graph to create a more detailed and stable analysis, overcoming limitations of existing techniques that rely on limited structural examinations. The researchers developed two models utilizing this new topological data: a machine learning model and a hybrid framework integrated with graph neural networks. The machine learning model achieves accuracy comparable to, or exceeding, existing methods based on kernel or degree-based filtration.

Incorporating this approach into graph neural networks yields performance improvements ranging from 0.4 to 21 percent across several benchmark datasets, and up to 8.2 percentage points over standard architectures. The authors acknowledge that the computational cost of identifying frequent subgraphs remains a limitation, particularly for very large graphs, and suggest future optimization. They also propose exploring the application of this method to other data types, potentially broadening its impact across various scientific disciplines.