Applied & Computational Mathematics seminar: Data-Adaptive Partitioning Algorithms, Extensions, and Applications

Speaker: Guy Oldaker, George Mason University

Title:  Data-Adaptive Partitioning Algorithms, Extensions, and Applications

Abstract:  Data-partitioning algorithms continue to be valuable tools with a broad range of application areas that include linear and dynamical systems, graph theory, and clustering.  Many of these methods can be cast in terms of Voronoi tessellations, where the data are partitioned into disjoint sets/regions defined by local neighborhoods of representative points/objects.  In this talk, we will discuss new and existing generalizations of the Voronoi tessellation and their applications to different fields.  Particular emphasis will be on the Centroidal Voronoi Orthogonal Decomposition (CVOD) and a new, adaptive variant that exhibits skill at automatically uncovering problem parameters directly from data (e.g., the number of subspaces and their dimensions in the subspace clustering problem).  We will also introduce a parameterized family of partitioning algorithms that includes several well-known methods like k-means, k-subspaces, and principal component analysis (PCA) as special cases.  Lastly, we will show how this family can be combined with ideas from simulated annealing to form a competitive pre-processing technique for the subspace clustering problem.  Theoretical results will be given throughout, as well as numerical experiments involving each of the methods discussed on problems taken from matrix approximation, dimensionality reduction, model order reduction (MOR), and subspace clustering.

Time:  Friday, April 4 – 1:30pm – 2:30pm

Place:  Exploratory Hall, room 4106