Additive Partial Matchings Induced by Persistence Morphisms
Additive Partial Matchings Induced by Persistence Morphisms
复制标题
持久态射引起的加性部分匹配
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
M. Soriano
中科院分区：
文献类型：
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作者：
Rocio Gonzalez;M. Soriano
给定一个持久化模块的态射（也称为$f：V（V）
8箭头U$，我们介绍了一种新的运营商，确定$V$和$U$诱导的条形码之间的部分匹配$f$。我们表明，建议的运营商是添加剂的持久态射的直和，它包含更多的信息比$f V$和秩不变。我们还说明了使用我们的诱导部分匹配的鲍尔-Lesnick部分匹配$chi_f$。最后，我们提供了一个家庭的持久性态射，包含模块建立从莫尔斯过滤，其中$chi_f$，秩不变和我们提出的诱导部分匹配是等价的。
Given a morphism of persistence modules (a.k.a. persistence morphism) $f : V
ightarrow U$, we introduce a novel operator that determines a partial matching between the barcodes of $V$ and $U$ induced by $f$. We show that the proposed operator is additive with respect to the direct sum of persistence morphisms, and that it contains more information than $f V$ and the rank invariant. We also illustrate some advantages of using our induced partial matching over the Bauer-Lesnick partial matching $chi_f$. Lastly, we provide a family of persistence morphisms that contain modules built from Morse filtrations, for which $chi_f$, the rank invariant and our proposed induced partial matching are equivalent.