论文标题
超图的ollivier-Ricci曲率：一个统一的框架
Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework
论文作者
论文摘要
桥接几何和拓扑，曲率是一个强大而富有表现力的不变。虽然曲率的效用在理论上和经验上已经在歧管和图表的背景下得到了证实，但其对新兴超图域的概括在很大程度上仍未得到探索。在图上，Ollivier-Ricci曲率测量了通过Wasserstein距离随机步行之间的差异，从而从概率理论和最佳运输中扎根了思想中的几何概念。我们开发了兰花，这是一个灵活的框架，将曲线曲率推广到超图，并证明所得曲线具有有利的理论特性。通过对来自不同领域的合成和现实世界超图的广泛实验，我们证明了兰花曲线在实践中执行各种超刻度任务既可扩展又有用。
Bridging geometry and topology, curvature is a powerful and expressive invariant. While the utility of curvature has been theoretically and empirically confirmed in the context of manifolds and graphs, its generalization to the emerging domain of hypergraphs has remained largely unexplored. On graphs, the Ollivier-Ricci curvature measures differences between random walks via Wasserstein distances, thus grounding a geometric concept in ideas from probability theory and optimal transport. We develop ORCHID, a flexible framework generalizing Ollivier-Ricci curvature to hypergraphs, and prove that the resulting curvatures have favorable theoretical properties. Through extensive experiments on synthetic and real-world hypergraphs from different domains, we demonstrate that ORCHID curvatures are both scalable and useful to perform a variety of hypergraph tasks in practice.
