[Compstats] Wed Feb 24 @ 4pm: Ali Ghodsi (part II)

Pascal Poupart ppoupart at cs.uwaterloo.ca
Tue Feb 16 18:43:16 EST 2010

Hi everyone,

There won't be any compstats seminar tomorrow since it is the reading 
break.  Ali Ghodsi will give part II of his talk next week (Wed Feb 24) 
@ 4pm in the AI lab.


Title: Learning a non-parametric mapping  for Non-linear
Dimensionality Reduction (part II)

Speaker: Ali Ghodsi
Date: Wed Feb 24
Time: 4 pm
Location: AI lab (DC2306C)

The foremost nonlinear dimensionality reduction algorithms provide an
embedding only for the given training data, with no straightforward
extension for the test
points. This shortcoming makes them unsuitable for problems such as
classification and regression. On the other hand, linear
dimensionality reduction algorithms are capable of handling the
out-of-sample examples easily, but their effectiveness is limited by
the linearity of the subspace they reveal. In this talk I propose a
novel dimensionality reduction algorithm which learns a parametric
mapping between the high-dimensional space and the embedded space. The
key observation is that when the dimensionality of the data is greater
than its quantity, it is always possible to find a linear
transformation that preserves a given subset of distances, while
changing the distances of another subset. We present a method that
first maps the points into a high-dimensional feature space, and then
explicitly searches for an affine transformation that preserves the
local distances while pulling the non-neighbor points as far apart as
possible. We formulate this search as an instance of semi-definite
programming. The resulted transformation can then be used to map
out-of-sample points into the embedded space.

This is a joint work with Pooyan Khajehpour

Pascal Poupart
Associate Professor
David R. Cheriton School of Computer Science
University of Waterloo
200 University Avenue West
Waterloo, Ontario
Canada N2L 3G1
Web: http://www.cs.uwaterloo.ca/~ppoupart
Email: ppoupart at cs.uwaterloo.ca 
Telephone: 1-519-888-4567x36239 
Fax: 1-519-885-1208

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