# Speaker: Partha Niyogi

## A Geometric Perspective on Learning Theory and Algorithms

### Abstract

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.

### Speaker Bio

Partha Niyogi
(http://people.cs.uchicago.edu/~niyogi)
is Professor in Computer Science and Statistics at The University of Chicago.
His research interests are in the general area of artificial intelligence with
a particular focus on problems in machine learning, speech, and computational
linguistics. He has a B.Tech. from
IIT, Delhi, and
SM. and Ph.D. from MIT.

Maintainer is

Jack Mostow
Last
modified: 9/26/2005 2:54 PM