Chromatic topological data analysis

preprint Chromatic topological data analysis submitted Sebastiano Cultrera di Montesano author 34D2A09C-F248-11E8-B48F-1D18A9856A870000-0001-6249-0832 Ondrej Draganov author 2B23F01E-F248-11E8-B48F-1D18A9856A870000-0003-0464-3823 Herbert Edelsbrunner author 3FB178DA-F248-11E8-B48F-1D18A9856A870000-0002-9823-6833 Morteza Saghafian author f86f7148-b140-11ec-9577-95435b8df824 GradSch department HeEd department 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. 2024 eng arXiv 2406.0410210.48550/ARXIV.2406.04102 Cultrera di Montesano, Sebastiano, et al. “Chromatic Topological Data Analysis.” ArXiv, 2406.04102, doi:<a href="https://doi.org/10.48550/ARXIV.2406.04102">10.48550/ARXIV.2406.04102</a>. S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.). Cultrera di Montesano, Sebastiano, Ondrej Draganov, Herbert Edelsbrunner, and Morteza Saghafian. “Chromatic Topological Data Analysis.” ArXiv, n.d. <a href="https://doi.org/10.48550/ARXIV.2406.04102">https://doi.org/10.48550/ARXIV.2406.04102</a>. S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, and M. Saghafian, “Chromatic topological data analysis,” arXiv. . Cultrera di Montesano, S., Draganov, O., Edelsbrunner, H., & Saghafian, M. (n.d.). Chromatic topological data analysis. arXiv. <a href="https://doi.org/10.48550/ARXIV.2406.04102">https://doi.org/10.48550/ARXIV.2406.04102</a> Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic topological data analysis. arXiv. doi:<a href="https://doi.org/10.48550/ARXIV.2406.04102">10.48550/ARXIV.2406.04102</a> Cultrera di Montesano S, Draganov O, Edelsbrunner H, Saghafian M. Chromatic topological data analysis. arXiv, 2406.04102. 189992025-02-04T16:21:21Z2025-02-10T08:14:27Z