论文标题
编辑距离和持久图上的图表
Edit Distance and Persistence Diagrams Over Lattices
论文作者
论文摘要
我们为持续的同源性构建了功能管道。该管道的输入是由任何有限度量晶格索引的过滤简单复合物，输出是持久图，定义为Möbius的出生死亡功能。我们将REEB图编辑距离调整到我们的每个类别中，并证明我们管道中的两个函数都是$ 1 $ -LIPSCHITZ，使我们的管道稳定。我们的构造概括了经典的持久图，在这种情况下，瓶颈距离非常等同于编辑距离。
We build a functorial pipeline for persistent homology. The input to this pipeline is a filtered simplicial complex indexed by any finite metric lattice and the output is a persistence diagram defined as the Möbius inversion of its birth-death function. We adapt the Reeb graph edit distance to each of our categories and prove that both functors in our pipeline are $1$-Lipschitz making our pipeline stable. Our constructions generalize the classical persistence diagram and, in this setting, the bottleneck distance is strongly equivalent to the edit distance.
