Mapper–Type Algorithms for Complex Data and Relations

Abstract

Mapper and Ball Mapper are Topological Data Analysis tools used for exploring high dimensional point clouds and visualizing scalar–valued functions on those point clouds. Inspired by open questions in knot theory, new features are added to Ball Mapper that enable encoding of the structure, internal relations and symmetries of the point cloud. Moreover, the strengths of Mapper and Ball Mapper constructions are combined to create a tool for comparing high dimensional data descriptors of a single dataset. This new hybrid algorithm, Mapper on Ball Mapper, is applicable to high dimensional lens functions. As a proof of concept we include applications to knot and game theory.

KEYWORDS:

• Dimension reduction
• Exploratory data analysis
• Topological data analysis
• Visualization

Disclosure Statement

The authors declare no competing interests.

Additional information

Funding

PD and DG acknowledge support by Dioscuri program initiated by the Max Planck Society, jointly managed with the National Science Centre (Poland), and mutually funded by the Polish Ministry of Science and Higher Education and the German Federal Ministry of Education and Research. DG is also with the University of Warsaw within the Doctoral School of Exact and Natural Sciences. RS is partially supported by NSF grant DMS-1854705.