Persistent homology is a popular data analysis technique that is used to capture the changing homology of an indexed sequence of simplicial complexes. These changes are summarized in persistence diagrams. A natural problem is to contract edges in complexes in the initial sequence to obtain a sequence of simplified complexes while controlling the perturbation between the original and simplified persistence diagrams. This paper is an extended version of Dey and Slechta (in: Discrete geometry for computer imagery, Springer, New York, 2019), where we developed two contraction operators for the case where the initial sequence is a filtration. In addition to the content in the original version, this paper presents proofs relevant to the filtration case and develops contraction operators for towers and multiparameter filtrations.

中文翻译：

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通过边缘收缩简化持久同源性的过滤

持久同源性是一种流行的数据分析技术，用于捕获简单复合体索引序列的变化同源性。这些更改总结在持久性图中。一个自然的问题是在初始序列中收缩复合体的边缘以获得简化的复合体序列，同时控制原始和简化的持久性图之间的扰动。本文是Dey和Slechta的扩展版本（在：计算机图像的离散几何，Springer，纽约，2019），其中我们针对初始序列是过滤的情况开发了两个收缩算子。除了原始版本中的内容外，本文还提供了与过滤情况有关的证明，并开发了塔和多参数过滤的收缩算子。