论文标题
持续的路径拉普拉斯
Persistent Path Laplacian
论文作者
论文摘要
S.-T.Yau及其同事提出的路径同源性为有向图和网络提供了一个新的数学模型。持续的路径同源性（PPH）通过过滤扩展了路径同源性，以处理不对称结构。但是，PPH被限制为纯粹的拓扑持久性，无法跟踪过滤过程中数据的同型形状演变。为了克服PPH的限制，引入了持久的路径拉普拉斯（PPL）以捕获数据的形状演化。 PPL的谐波光谱完全恢复了PPH的拓扑持久性，其非谐波光谱揭示了在过滤过程中数据的同型形状演变。
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.
