[Ml-stat-talks] IDeAS Seminar Tuesday 9/20 - Daniel Kaslovsky
Amit Singer
amits at math.Princeton.EDU
Thu Sep 15 10:54:44 EDT 2011
The first IDeAS Seminar will take place on Tuesday 9/20/11 @ 1:30 PM in the
Joseph Henry Room - Jadwin Hall.
Below is the information
Date: Tuesday 9/20/11
Time: 1:30 pm
Place: Joseph Henry Room - Jadwin Hall
Speaker: Daniel Kaslovsky - University of Colorado - Boulder
Title: Optimal Tangent Plane Recovery from Noisy Manifold Samples
Abstract:
Efficient data processing algorithms may be realized by exploiting the
low-dimensional manifold structure often inherent in a data set. We seek
efficient parameterizations of such data sets via projection into
appropriate manifold tangent planes. Parameterizing a data set thus becomes
a problem of estimating local tangent planes from noisy manifold samples.
Principal component analysis (PCA) is often the tool of choice, as it
returns an optimal basis in the case of noise-free samples from a linear
subspace. To process noisy data, PCA must be applied locally, at a scale
small enough such that the manifold is approximately linear, but at a scale
large enough such that structure may be discerned from noise. We present our
approach that uses the geometry of the data to guide our definition of
locality, discovering the optimal balance of this noise-curvature trade-off.
Using perturbation theory of eigenspaces, we study the stability of the
subspace estimated by PCA as a function of scale, and bound (with high
probability) the angle it forms with the true tangent space. By adaptively
selecting the scale that minimizes this bound, our analysis reveals the
optimal scale for local tangent plane recovery. Applications are discussed,
with a focus on image processing.
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