编辑格上的距离和持久性图

IF 1.6 2区 数学 Q2 MATHEMATICS, APPLIED SIAM Journal on Applied Algebra and Geometry Pub Date : 2020-10-14 DOI:10.1137/20M1373700
Alex McCleary, A. Patel
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引用次数: 31

摘要

我们为持久同源构建了一个功能管道。该管道的输入是由任意有限格索引的过滤简单复形,输出是定义为某单调积分函数的莫比乌斯反演的持久图。我们将Landi等人的Reeb图编辑距离适用于我们的每个类别,并证明了我们管道中的两个函子都是1-Lipschitz,使得我们的管道稳定。
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Edit Distance and Persistence Diagrams Over Lattices
We build a functorial pipeline for persistent homology. The input to this pipeline is a filtered simplicial complex indexed by any finite lattice, and the output is a persistence diagram defined as the Mobius inversion of a certain monotone integral function. We adapt the Reeb graph edit distance of Landi et. al. to each of our categories and prove that both functors in our pipeline are 1-Lipschitz making our pipeline stable.
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
19
期刊最新文献
Erratum: A Counterexample to Comon’s Conjecture Computing Geometric Feature Sizes for Algebraic Manifolds A Sum of Squares Characterization of Perfect Graphs Persistent Homology of Semialgebraic Sets Finiteness of Spatial Central Configurations with Fixed Subconfigurations
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