ECE Seminar: Distorted Diffeomorphisms of Small Distortion in Euclidean Space and their Applications to the Parsimonious Representation of Data in Manifold Learning
Friday, February 8, 2013 - 4:00pm to 5:00pm
Steven B. Damelin, Ph.D., Wayne Country Day School, Goldsboro, North Carolina
The parsimonious representation of data is a fundamental problem in many sciences. By this problem, we typically mean, obtaining accurate models of naturally occurring sources of data, obtaining optimal representations of such models and rapidly computing such optimal representations. A basic question which interests us in this talk is when do two sets of point clouds in some containing high dimensional Euclidean space describe the same manifold? We will address this question now in some sense by talking about our joint work with Charlie Fefferman. BIOGRAPHY: Ph.D., University of the Witwatersrand (1996). Teaching and Research Positions: University of South Florida, The Pennsylvania State University, the Institute for Mathematics and its Applications, University of Minnesota, Georgia Southern University, University of the Witwatersrand and at private schools both in South Africa and the United States. 71 research papers in the following areas: Computer Vision, Imaging, Signal Processing, Computational Harmonic Analysis, Statistical Inference, Orthogonal Polynomials, Potential Theory, Random Matrices, Approximation Theory, Numerical Analysis, Geometric Analysis, Coding Theory. Member of the American Mathematical Society Mathematics Research Communities Advisory Board, the American Mathematical Society Committee of Committees, a New Directions Research Professor at the Interdisciplinary Institute of Mathematics its Applications, University of Minnesota.