色度拓扑数据分析

arXiv - CS - Computational Geometry Pub Date : 2024-06-06 DOI:arxiv-2406.04102

Sebastiano Cultrera di Montesano, Ondrej Draganov, Herbert Edelsbrunner, Morteza Saghafian

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引用次数: 0

摘要

自 TDA（拓扑数据分析的简称）诞生以来，探索点配置的形状一直是推动其发展的关键因素。本调查说明了最近在拓宽这些想法以模拟多个配置（每个配置用颜色区分）之间的空间交互方面所做的努力。它描述了这一领域的进展，并通过提及尚未解决的问题和有前景的研究途径，为进一步探索奠定了基础，同时重点介绍了与离散几何的重叠。

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Chromatic Topological Data Analysis

Exploring the shape of point configurations has been a key driver in the evolution of TDA (short for topological data analysis) since its infancy. This survey illustrates the recent efforts to broaden these ideas to model spatial interactions among multiple configurations, each distinguished by a color. It describes advances in this area and prepares the ground for further exploration by mentioning unresolved questions and promising research avenues while focusing on the overlap with discrete geometry.

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arXiv - CS - Computational Geometry

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