Scientific Computing Seminar

Date:

Monday, December 15, 2003

Time:

1:00pm-2:00pm

Location:

50A-5132

Seminar Speaker:

Hongyuan Zha
Associate Professor
Department of Computer Science and Engineering
The Pennsylvania State University
http://www.cse.psu.edu/~zha/

Title:

Isometric Embedding and Manifold Learning

Abstract:

Recently, the Isomap algorithm has been proposed for learning a parameterized manifold from a set of unorganized samples from the manifold. It is based on extending the classical multidimensional scaling method for dimension reduction, replacing Euclidean distances by the geodesic distances on the manifold. In this talk, after presenting some tutorial materials on manifold learning and Isomap we discuss a continuous version of Isomap which we call continuum Isomap and show that manifold learning in the continuous framework is reduced to an eigenvalue problem of an integral operator. We also show that the continuum isomap can perfectly recover the underlying parameterization if the mapping associated with the parameterized manifold is an isometry and its domain is convex. We finally show the continuum Isomap also provides a natural way to compute low-dimensional embedding for out-of-sample data points, and derive some bounds for the case when the isometry condition is violated. Several numerical examples are given to illustrate the algorithm.

Sponsor of Seminar:

Chris Ding

Scientific Computing

Contact Esmond G. Ng EGNg@lbl.gov