持久路径拉普拉斯算子。

IF 1.7 Q2 MATHEMATICS, APPLIED
Rui Wang, Guo-Wei Wei
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引用次数: 13

摘要

Yau及其同事提出的路径同调为有向图和网络提供了一个新的数学模型。持久路径同源性(PPH)通过过滤来扩展路径同源性,以处理不对称结构。然而,PPH受限于纯拓扑持久性,并且不能在过滤过程中跟踪数据的同位形状演化。为了克服PPH的局限性,引入了持久路径拉普拉斯算子(PPL)来捕捉数据的形状演化。PPL的调和谱完全恢复了PPH的拓扑持久性,其非调和谱揭示了过滤过程中数据的同位形状演化。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
PERSISTENT PATH LAPLACIAN.

Path homology proposed by S.-T.Yau and his co-workers provides a new mathematical model for directed graphs and networks. Persistent path homology (PPH) extends the path homology with filtration to deal with asymmetry structures. However, PPH is constrained to purely topological persistence and cannot track the homotopic shape evolution of data during filtration. To overcome the limitation of PPH, persistent path Laplacian (PPL) is introduced to capture the shape evolution of data. PPL's harmonic spectra fully recover PPH's topological persistence and its non-harmonic spectra reveal the homotopic shape evolution of data during filtration.

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CiteScore
3.30
自引率
0.00%
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