[Colloquium] Today: He/Dissertation Defense/10-27-05

[Margaret Jaffey]

This is a reminder about Xiaofei He's dissertation defense this  
afternoon.

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   Department of Computer Science/The University of Chicago

                             *** Dissertation Defense ***


Candidate:  Xiaofei He

Date:  Thursday, October 27, 2005

Time and Location:  3:00 p.m. in Ryerson 251

Title:  Locality Preserving Projections

Abstract:
Many problems in information processing involve
some form of dimensionality reduction. In this thesis, we introduce
Locality Preserving Projections (LPP). These are linear projective
maps that arise by solving a variational problem that optimally
preserves the neighborhood structure of the data set. LPP should be
seen as an alternative to Principal Component Analysis (PCA) -- a
classical linear technique that projects the data along the
directions of maximal variance. When the high dimensional data lies
on a low dimensional manifold embedded in the ambient space, the
Locality Preserving Projections are obtained by finding the optimal
linear approximations to the eigenfunctions of the Laplace Beltrami
operator on the manifold. As a result, LPP shares many of the data
representation properties of nonlinear techniques such as Laplacian
Eigenmaps or Locally Linear Embedding. Yet LPP is linear and more
crucially is defined everywhere in ambient space rather than just on
the training data points. Theoretical analysis shows that PCA, LPP,
and Linear Discriminant Analysis (LDA) can be obtained from
different graph models. Central to this is a graph structure that is
inferred on the data points. LPP finds a projection that respects
this graph structure. Based on the locality preserving criterion, we
also present a new feature selection algorithm which is based on the
observation that, two data points probably share the same label if
they are sufficiently close to each other. The importance of a
feature is evaluated by its power of locality preserving, or,
Laplacian Score. We have applied our algorithms to several real
world applications, e.g. face recognition and document
representation.

Candidate's Advisor: Prof. Partha Niyogi

A draft copy of Mr. He's dissertation is available soon in Ry 161A.


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Margaret P. Jaffey                             margaret at cs.uchicago.edu
Department of Computer Science
Student Support Rep (Ry 161A)        (773) 702-6011
The University of Chicago                  http://www.cs.uchicago.edu
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