Explore advanced mathematical concepts for data visualization in this lecture from the CMSA Mathematics and Machine Learning Closing Workshop, where Max Planck Institute's Jürgen Jost presents innovative approaches combining category theory and geometry. Learn how high-dimensional data can be effectively represented on lower-dimensional Riemannian manifolds, despite inherent complexities and curvatures. Discover the mathematical foundations underlying visualization techniques like UMAP and examine an enhanced methodology for reducing data dimensions to manageable 2D or 3D representations. Gain insights into how intrinsic constraints and regularities in data can be leveraged for more effective visualization strategies.
Overview
Syllabus
Jürgen Jost | Data visualization with category theory and geometry
Taught by
Harvard CMSA
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