单参数持久性的度量和稳定性

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Applied Algebra and Geometry Pub Date : 2019-04-05 DOI:10.1137/19m1243932

W. Chachólski, H. Riihimäki

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引用次数: 13

摘要

我们提出了一种考虑单参数持久性的新方法。我们相信拓扑持久性从根本上讲与分解定理无关，而是由度量的选择所起的核心作用。在持久向量空间之间选择一个伪度量可以稳定离散不变量。我们在此稳定化和稳定秩不变量背后发展了理论。我们在具体的数据分析中给出了这种方法的有用性的证据。

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Metrics and Stabilization in One Parameter Persistence

We propose a new way of thinking about one parameter persistence. We believe topological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between persistent vector spaces leads to stabilization of discrete invariants. We develop theory behind this stabilization and stable rank invariant. We give evidence of the usefulness of this approach in concrete data analysis.

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来源期刊

SIAM Journal on Applied Algebra and Geometry MATHEMATICS, APPLIED-

CiteScore

2.20

自引率

0.00%

发文量