[Colloquium] Reminder: Zhou/Dissertation Defense/Oct 19, 2011

[Margaret Jaffey]

This is a reminder about Xueyuan's defense tomorrow.

       Department of Computer Science/The University of Chicago

                     *** Dissertation Defense ***


Candidate:  Xueyuan Zhou

Date:  Wednesday, October 19, 2011

Time:  3:00 PM

Place:  Ryerson 276

Title: Learning Functions on Unknown Manifolds

Abstract:
As more and more complex data sources become available, the analysis
of graph and manifold data has become an essential part of various
sciences. In this thesis, learning a function through samples on a
manifold is investigated. Toward this goal, several problems are
studied. First, regularization in Sobolev spaces on manifolds are
discussed, which can be used to find a smooth function on the data
manifold. The regularizer is implemented by iterated Laplacian, which
is a natural tool to study Sobolev spaces on manifolds. This way of
regularization generalizes thin plate splines from regular grid on a
known domain to random samples on an unknown manifold. Second, we
study the asymptotic behavior of graph Laplacian eigenmaps method,
which is the finite-dimensional approximation of an
infinite-dimensional problem. The analysis shows that the method, as a
nonparametric regression method, achieves the optimal integrated mean
squares error rate in terms of the intrinsic dimensionality of the
manifold. Third, the limit behavior of graph Laplacian on a manifold
boundary and its implications are discussed. Finally, we studied a
ranking on data manifold algorithm in information retrieval from a
functional analysis point of view, which goes beyond the physics-based
intuition.

Xueyuan's advisors are Prof. Pedro Felzenszwalb and Prof. Mikhail Belkin

Login to the Computer Science Department website for details,
including a draft copy of the dissertation:

 https://www.cs.uchicago.edu/phd/phd_announcements#zhouxy

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Margaret P. Jaffey            margaret at cs.uchicago.edu
Department of Computer Science
Student Support Rep (Ry 156)               (773) 702-6011
The University of Chicago      http://www.cs.uchicago.edu
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