IsUMap: An improved method for data visualization and dimension reduction, and the mathematics behind it
- Jürgen Jost
Abstract
Data may contain some unknown structure and may seem high dimensional. There exist various schemes for extracting dominant structures and efficiently representing them in 2D. A currently very popular scheme is UMAP. We clarify the underlying mathematics and introduce some new geometric ideas and on that basis develop an improved method.
References:
P.Joharinad, J.Jost: Mathematical principles of topological and geometric data analysis, Monograph, Math of Data, Springer, 2023
L.Barth, H.Fahimi, P.Joharinad, J.Jost, J.Keck: Data visualization with category theory and geometry, Monograph, Math of Data, Springer, 2025
L.Barth, H.Fahimi, P.Joharinad, J.Jost, J.Keck: IsUMap: Manifold Learning and Data Visualization leveraging Vietoris-Rips filtrations, Proc. AAAI Conf. Artificial Intelligence 39 (2025); arXiv:2407.17835, with code
L.Barth, H.Fahimi, P.Joharinad, J.Jost, J.Keck: Fuzzy simplicial sets and their application to geometric data analysis Applied Categorical Structures 33 (2025); arXiv:2406.11154
L.Barth, H.Fahimi, P.Joharinad, J.Jost, J.Keck: Merging Hazy Sets with m-Schemes: A Geometric Approach to Data Visualization, Adv.Theor.Math.Physics (2026)
