使用边拉普拉斯动力学与里奇流进行社区检测

中文摘要 AI 辅助

已经发现，利用图动力学的几何性质可以揭示统计分析无法获取的数据关键信息。里奇流的性质以与光滑流形分解相同的方式揭示数据的隐藏动力学。在本文中，我们探索了里奇流的替代方案，发现可以使用更简单且定义明确的边拉普拉斯算子来实践图中的社区检测，从而引出类似的性质。此外，本方法获得的结果表明，由边拉普拉斯算子驱动的流产生的结果与里奇流相似。相比之下，计算Forman-Ricci曲率需要遍历相邻边，而计算Olivier-Ricci曲率涉及与图节点相关的Wasserstein距离和概率分布的计算，使得边拉普拉斯方法在计算上更高效。

英文摘要

It has been found that utilizing the geometric properties of the graph dynamics can bring out crucial information of the data that a statistical analysis will not. The properties of Ricci flow bring out hidden dynamics of the data in the same way as decomposition of smooth manifolds. In this paper we explore an alternative to Ricci flow, where we find that we can bring out similar properties like it using a simpler and well defined Edge Laplacian to practice community detection in graphs. Moreover, the results obtained by the present approach show that a flow driven by the Edge Laplacian yields results similar to those of the Ricci flow. In contrast, computing the Forman-Ricci curvature requires looping over the adjacent edges, while computing Olivier-Ricci curvature involves the computation of Wasserstein distance and probability distribution associated with the graph nodes, making the Edge Laplacian approach computationally more efficient.

发表机构

• Department of Computational and Data Sciences Indian Institute of Science (IISc)（计算与数据科学系 印度科学学院）

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