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Graduate Seminar
Jing Liu Carnegie Melllon University Title: Construction of centroidal Voronoi tessellations using a nonlinear conjugate gradient method based on trust regions Abstract: A Voronoi tessellation whose generating points coincide with the centroids (mass centers) of the corresponding Voronoi regions is called a centroidal Voronoi tessellation (CVT). Due to the natural optimization properties enjoyed by CVTs, they have diverse applications in many areas of science and engineering, for instance, image segmentation, quadrature, finite difference methods, cellular biology, statistics and territorial behavior of animals. Classic methods for computing CVTs, such as the Lloyd method and the MacQueen's kmeans method, are not efficient enough. In this talk, we study a new algorithm for computing CVTsthe conjugate gradient method based on trust regions (CGTR). This algorithm significantly speeds up the construction of CVTs. Numerical experiments are also conducted to substantiate theoretical analysis. Date: Friday, February 4, 2011 Time: 5:30 pm Location: Wean Hall 8220 Submitted by: Chris Almost 