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This colloquium talk by Juergen Jöst at the Topos Institute explores the mathematical foundations behind high-dimensional data visualization techniques. Discover how sophisticated tools from Riemannian geometry and category theory underpin popular visualization algorithms like UMAP. Learn about the development of an improved algorithm called IsUMap, which builds on rigorous mathematical theory. The presentation examines Spivak's fuzzy simplicial sets and their connection to Topological Data Analysis, showing how these category theoretical foundations provide conceptual tools for merging different generalized metric structures. Gain insights into the geometric and topological principles that enable effective visualization of complex high-dimensional data in two dimensions.
