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.

翻译：图嵌入在图表示学习中发挥着关键作用，使得机器学习模型能够探索和解释图结构数据。然而，现有方法通常依赖于不透明的高维嵌入，限制了可解释性和实际可视化效果。本文提出拓扑演化率（Topological Evolution Rate, TopER），一种基于拓扑数据分析的新型低维嵌入方法。TopER通过计算图子结构的演化率，简化了关键拓扑方法——持续同调，从而产生直观且可解释的图数据可视化。该方法不仅增强了对图数据集的探索能力，还在图聚类和分类任务中展现出具有竞争力的性能。我们基于TopER的模型在分子、生物和社交网络数据集上的分类、聚类及可视化任务中，达到或超越了当前最优结果。