Talk page
Title:
Fitting manifolds to data.
Speaker:
Abstract:
The problems come in two flavors.
Extrinsic Flavor: Given a point cloud in R^N sampled from an unknown probability density, how can we decide whether that probability density is concentrated near a low-dimensional manifold M with reasonable geometry? If such an M exists, how can we find it? (Joint work with S. Mitter and H. Narayanan)
Intrinsic Flavor: How can we decide whether a given finite metric space is approximately isometric (in an appropriate sense) to an epsilon-net in a manifold M with reasonable geometry? If such an M exists, how can we find it?
(Joint work with S.Ivanov, Y. Kurylev, M. Lassas and H. Narayanan)
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