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Chromatic Topological Data Analysis

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arxiv 2406.04102 v1 pith:ABLEGM22 submitted 2024-06-06 cs.CG

Sebastiano Cultrera di Montesano , Ondrej Draganov , Herbert Edelsbrunner , Morteza Saghafian This is my paper · ORCID
classification cs.CG
keywords analysisconfigurationsdatatopologicaladvancesareaavenuesbeen
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Intersection Euler Characteristic Profile: Euler Calculus and Stability for Topological Interaction of Ball Unions

    math.AT 2026-08 conditional novelty 6.0 of 10

    The Intersection Euler Characteristic Profile, the Euler characteristic of the common overlap of thickened point clouds, is shown to be the unique stable, canonical interaction invariant, with near-optimal algorithm a...

  2. Gromov-Hausdorff distance between chromatic metric pairs and stability of the six-pack

    math.MG 2025-07 conditional novelty 6.0 of 10

    Introduces the C-constrained Gromov-Hausdorff distance for chromatic metric pairs and proves that all six diagrams in a six-pack are stable in bottleneck distance with respect to it, up to a factor of 2.

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