# A Geometric Perspective on Learning Theory and Algorithms

## Partha Niyogi

### CS Dept. U of Chicago

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.
Bio
Partha Niyogi received his undergraduate degree from IIT Delhi and S.M. and
Ph.D. from MIT. After working at Bell Laboratories for a few years, he joined
The University of Chicago where he is currently Professor in the Departments
of Computer Science and Statistics. His research interests are in learning
theory and algorithms, statistical inference, computational linguistics, and
artificial intelligence.

Deepak Ramachandran
Last modified: Fri Aug 8 11:38:17 CST 2006