We discuss several problems concerning the geometry of data sets, where the ambient dimension runs from three (Physical Data Sets) to very large. Among the tools discussed are Diffusion Geometry and Multiscale Singular Value Decompositions ("Beta Numbers").
Some of this work is in collaboration with Gilad Lerman, Mauro Maggioni, and Raanan Schul. Mauro Maggioni will also give part of the presentation for this talk.
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