Department of Computer Science, Department of
Statistics, University of Chicago, USA
Friday 17 March 2006
15:00
Seminar Room B10 (Basement)
Alexandra
House, 17 Queen Square, London, WC1N 3AR
A Geometric Perspective on Learning Theory
and Algorithms
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 embedding, clustering, classification, and semi-supervised
learning will be considered.
