扩散框架下的超图拉普拉斯算子
Hypergraph Laplacians in Diffusion Framework
摘要：
网络是用于对发生交互的复杂系统进行建模的重要结构。在基本网络模型中，实体被表示为节点，并且它们之间的交互和关系被表示为边。然而，在一个复杂的系统中，我们不能把所有的关系都描述为成对的相互作用，而应该描述为高阶的相互作用。超图被成功地用于模拟复杂系统中的高阶相互作用。本文在扩散框架下提出了两个新的超图拉普拉斯算子。我们的拉普拉斯算子考虑了高阶相互作用之间的关系，因此不仅可以用来模拟超图上顶点之间的扩散，还可以用来模拟高阶结构之间的扩散。这些拉普拉斯算子可以用于超图上的不同网络挖掘问题，例如超图上的社会传染模型，超图上的影响研究和超图分类。
英文摘要：
Networks are important structures used to model complex systems where interactions take place. In a basic network model, entities are represented as nodes, and interaction and relations among them are represented as edges. However, in a complex system, we cannot describe all relations as pairwise interactions, rather should describe as higher-order interactions. Hypergraphs are successfully used to model higher-order interactions in complex systems. In this paper, we present two new hypergraph Laplacians based on diffusion framework. Our Laplacians take the relations between higher-order interactions into consideration, hence can be used to model diffusion on hypergraphs not only between vertices but also higher-order structures. These Laplacians can be employed in different network mining problems on hypergraphs, such as social contagion models on hypergraphs, influence study on hypergraphs, and hypergraph classification, to list a few.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
