Kronecker PCA: A covariance decomposition for high dimensional data
Prof. Alfred Hero, IEEE Fellow, R. Jamison and Betty Williams Professor of Engineering
Department of Electrical Engineering and Computer Science, University of Michigan
Monday, February 24, 2014, 3:15 PM
Goldwater Center (GWC) 487 [map]
Abstract
Kronecker covariance decompositions can be interpreted as a generalization of the matrix singular value decomposition (SVD) where the components are Kronecker product matrices. While these components are not orthogonal, the number of Kronecker components, called the Kronecker separation rank, of the decomposition plays a similar role as the rank in low rank covariance matrix approximation. We obtain high dimensional convergence rates on the approximation error of the Kronecker decomposition under a Wishart sample covariance model as a function of the number of free variables p and the number of independent samples n. We illustrate the power of Kronecker covariance decompositions for spatio-temporal data applications in sensor networks and video processing.
Biosketch
Alfred O. Hero III received a B.S. (summa cum laude) from Boston University (1980) and a Ph.D from Princeton University (1984), both in electrical engineering. Since 1984 he has been with the University of Michigan, Ann Arbor, where he is the R. Jamison and Betty Williams Professor of Engineering. At the University of Michigan his primary appointment is in the Department of Electrical Engineering and Computer Science and he also has appointments, by courtesy, in the Department of Biomedical Engineering and the Department of Statistics. From 2008 to 2013 he held the Digiteo Chaire d’Excellence, sponsored by Digiteo Research Park in Paris, located at the Ecole Superieure d’Electricite, Gif-sur-Yvette, France. He has held other visiting positions at LIDS Massachusetts Institute of Technology (2006), Boston University (2006), I3S University of Nice, Sophia-Antipolis, France (2001), Ecole Normale Superieure de Lyon (1999), Ecole Nationale Superieure des Telecommunications, Paris (1999), Lucent Bell Laboratories (1999), Scientific Research Labs of the Ford Motor Company, Dearborn, Michigan (1993), Ecole Nationale Superieure des Techniques Avancees (ENSTA), Ecole Superieure d’Electricite, Paris (1990), and M.I.T. Lincoln Laboratory (1987 – 1989).
