A Theory of Sub-Barcodes
A Theory of Sub-Barcodes
复制标题
子条形码理论
DOI：
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Don Sheehy
中科院分区：
文献类型：
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作者：
Oliver A. Chubet;Kirk P. Gardner;Don Sheehy
从Bauer和Lesnick的工作中，我们知道从逐点有限维持久性模的范畴到条形码和重叠匹配的范畴之间不存在函子。在这项工作中，我们介绍了子条形码，并表明，有一个函子从持久性模块同态的因式分解的类别的一个偏序集的条形码排序的子条形码的关系。子条形码和因子分解为瓶颈匹配和交织提供了一种更宽松的替代方案，可以在拓扑数据分析中自然出现的许多设置中提供强有力的保证。子条形码的主要用途是在没有交织的情况下对未知条形码进行强有力的声明。例如，仅给定未知实值函数f的上界和下界g ≥ f ≥（cid：96），可以仅从（cid：96）和g构建与f相关联的子条形码。我们提出了一个理论的子条形码和观察函子范畴Fun（Int op，Mch）中的subobliterature自然对应于子条形码。
From the work of Bauer and Lesnick, it is known that there is no functor from the category of pointwise finite-dimensional persistence modules to the category of barcodes and overlap matchings . In this work, we introduce sub-barcodes and show that there is a functor from the category of factorizations of persistence module homomorphisms to a poset of barcodes ordered by the sub-barcode relation . Sub-barcodes and factorizations provide a looser alternative to bottleneck matchings and interleavings that can give strong guarantees in a number of settings that arise naturally in topological data analysis. The main use of sub-barcodes is to make strong claims about an unknown barcode in the absence of an interleaving. For example, given only upper and lower bounds g ≥ f ≥ (cid:96) of an unknown real-valued function f , a sub-barcode associated with f can be constructed from (cid:96) and g alone. We propose a theory of sub-barcodes and observe that the subobjects in the functor category Fun ( Int op , Mch ) naturally correspond to sub-barcodes.
DOI：
10.1007/s41468-018-0012-6
发表时间：
2018
期刊：
Journal of Applied and Computational Topology
影响因子：
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作者：
Patel, Amit
通讯作者：
Patel, Amit