用拓扑演化率实现可解释的低维图嵌入
TopER: Topological Embeddings in Graph Representation Learning
- 基于拓扑数据分析，计算图子结构演化速率
- 在分子、生物和社交网络数据上表现达顶尖水平
- 结果直观可解释，适合需要可视化分析的场景
图嵌入在图表示学习中起关键作用，使机器学习模型能够探索和理解图结构数据。然而，现有方法常依赖于难以解释的高维嵌入，限制了可解释性和实际可视化。本文提出拓扑演化率（TopER），一种基于拓扑数据分析的新型低维嵌入方法。通过简化持久同调（Persistent Homology）的核心思想，计算图子结构的演化速率，实现对图数据的直观、可解释的可视化。该方法不仅提升了图数据的探索能力，还在图聚类和分类任务中表现优异。基于TopER的模型在分子、生物和社交网络数据集上的分类、聚类和可视化任务中达到或超越当前最优水平。
原文摘要 · Abstract (English)
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.
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