Chromatic Topological Data Analysis

TL;DR

This paper surveys recent developments in chromatic topological data analysis, which extends traditional TDA to analyze spatial interactions among multiple colored point configurations, highlighting advances, open questions, and future research directions.

Contribution

It introduces the concept of chromatic TDA, connecting topological data analysis with discrete geometry to model interactions among multiple configurations distinguished by color.

Findings

Advances in modeling spatial interactions among multiple configurations.

Identification of unresolved questions in chromatic TDA.

Potential research avenues linking TDA and discrete geometry.

Abstract

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.