任何图表都是映射图表

arXiv - MATH - Algebraic Topology Pub Date : 2024-08-20 DOI:arxiv-2408.11180

Enrique G Alvarado, Robin Belton, Kang-Ju Lee, Sourabh Palande, Sarah Percival, Emilie Purvine, Sarah Tymochko

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引用次数: 0

摘要

Mapper 算法是拓扑数据分析中可视化和数据探索的常用工具。我们研究了 Mapperal 算法的一个逆问题：给定一个数据集 $X$ 和一个图 $G$，是否存在一组 Mapper 参数，使得 $X$ 的输出 Mapper 图与 $G$ 同构？我们提供了能肯定回答这一问题的构造。我们的结果表明，可以通过设计 Mapper 参数来生成所需的图形。

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Any Graph is a Mapper Graph

The Mapper algorithm is a popular tool for visualization and data exploration in topological data analysis. We investigate an inverse problem for the Mapper algorithm: Given a dataset $X$ and a graph $G$, does there exist a set of Mapper parameters such that the output Mapper graph of $X$ is isomorphic to $G$? We provide constructions that affirmatively answer this question. Our results demonstrate that it is possible to engineer Mapper parameters to generate a desired graph.

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arXiv - MATH - Algebraic Topology

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