A Geometric perspective on machine Learning

Monday, October 27, 2008 - 12:15pm - 1:05pm
EE/CS 3-180
Partha Niyogi (University of Chicago)
Increasingly, we face machine learning problems in very high
dimensional spaces. We proceed with the intuition that although
natural data lives in very high dimensions, they have relatively few
degrees of freedom. One way to formalize this intuition is to model
the data as lying on or near a low dimensional manifold embedded in
the high dimensional space. This point of view leads to a new class of
algorithms that are manifold motivated and a new set of theoretical
questions that surround their analysis. A central construction in
these algorithms is a graph or simplicial complex that is data-derived
and we will relate the geometry of these to the geometry of the
underlying manifold. Applications to data analysis, machine
learning, and numerical computation will be considered.
MSC Code: