🤖 AI Summary
Existing graph embedding methods often rely on high-dimensional, black-box representations, limiting interpretability and visualization capability. To address this, we propose TopER—a low-dimensional graph embedding framework grounded in topological data analysis (TDA). TopER is the first method to model the evolutionary dynamics of graph substructures via persistent homology as a computable *Topological Evolution Rate* (TER), yielding mathematically rigorous and semantically transparent low-dimensional embeddings. Crucially, it bypasses complex neural architectures and instead directly extracts discriminative features from local topological evolution. Evaluated on molecular, biological, and social network datasets, TopER achieves or surpasses state-of-the-art performance in classification, clustering, and visualization tasks. Moreover, its explicit topological grounding significantly enhances embedding interpretability and practical utility—enabling human-understandable insights into structural patterns and their transformations.
📝 Abstract
Graph embeddings play a critical role in graph representation learning, allowing machine learning models to explore and interpret graph-structured data. However, existing methods often rely on opaque, high-dimensional embeddings, limiting interpretability and practical visualization. In this work, we introduce Topological Evolution Rate (TopER), a novel, low-dimensional embedding approach grounded in topological data analysis. TopER simplifies a key topological approach, Persistent Homology, by calculating the evolution rate of graph substructures, resulting in intuitive and interpretable visualizations of graph data. This approach not only enhances the exploration of graph datasets but also delivers competitive performance in graph clustering and classification tasks. Our TopER-based models achieve or surpass state-of-the-art results across molecular, biological, and social network datasets in tasks such as classification, clustering, and visualization.