Speaker: Maria Emelianenko, GMU
Title: Centroidal Voronoi tessellations: recent advances in theory and applications
Abstract:
A centroidal Voronoi tessellation (CVT) is a special Voronoi
tessellation of a given set such that the associated generating points are
the centers of mass of the corresponding Voronoi regions with respect to a
pre-defined density function. CVTs enjoy natural optimization properties
which make them very popular in diverse scientific and engineering
applications that range from art design, astronomy, clustering, geometric
modeling, image and data analysis, resource optimization, quadrature design,
sensor networks, to numerical solution of partial di fferential equations.
In particular, CVTs have been widely used in the design of optimal vector
quantizers in electrical engineering. They are also related to the k-means
algorithm in clustering analysis. CVTs can be defined in more general cases
such as those constrained to a manifold, or those corresponding to
anisotropic metrics, and other abstract settings.This talk will give an
overview of current state-of-the-art in the area of theoretical analysis and
applications of CVTs, with the focus on recent convergence results and
acceleration schemes.
Place: Science and Technology Building I, Room 242
Refreshments will be served before the talk at 3:00 p.m. in Room 222.
Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491