Hypergraph Change Point Detection using Adapted Cardinality-Based Gadgets: Applications in Dynamic Legal Structures

Hiroki Matsumoto, Takahiro Yoshida, Ryoma Kondo, Ryohei Hisano
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Abstract

Hypergraphs provide a robust framework for modeling complex systems with higher-order interactions. However, analyzing them in dynamic settings presents significant computational challenges. To address this, we introduce a novel method that adapts the cardinality-based gadget to convert hypergraphs into strongly connected weighted directed graphs, complemented by a symmetrized combinatorial Laplacian. We demonstrate that the harmonic mean of the conductance and edge expansion of the original hypergraph can be upper-bounded by the conductance of the transformed directed graph, effectively preserving crucial cut information. Additionally, we analyze how the resulting Laplacian relates to that derived from the star expansion. Our approach was validated through change point detection experiments on both synthetic and real datasets, showing superior performance over clique and star expansions in maintaining spectral information in dynamic settings. Finally, we applied our method to analyze a dynamic legal hypergraph constructed from extensive United States court opinion data.
使用基于卡丁率的自适应小工具进行超图变化点检测:动态法律结构中的应用
超图为具有高阶交互作用的复杂系统建模提供了一个强大的框架。然而,在动态环境中分析超图却面临着巨大的计算挑战。为了解决这个问题,我们引入了一种新方法,通过对称组合拉普拉卡,调整基于万有引力的小工具,将超图转换成强连接的加权有向图。我们证明,原始超图的传导性和边扩展的调和平均值可以被转换后有向图的传导性限定,从而有效地保留了关键的切割信息。此外,我们还分析了所得到的拉普拉斯函数与星形扩展所得到的拉普拉斯函数之间的关系。我们的方法通过在合成数据集和真实数据集上进行的变化点检测实验得到了验证,结果表明,在动态环境下,我们的方法在保持光谱信息方面的性能优于簇扩展和星形扩展。最后,我们将我们的方法应用于分析由大量美国法院意见数据构建的动态法律超图。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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