Hamid KrimIEEE Fellow, SPS Distinguished Lecturer
North Carolina State Univ., USA
Field of interest: Communications and Signal Processing (Including Digital Communications, Digital Signal Processing, Image Analysis and Computer Vision), Control, Robotics and Mechatronics, Machine learning
Talk: Convexity, Sparsity, Nullity and all that….in Machine Leaning
Abstract: High dimensional data exhibit distinct properties compared to its low dimensional counterpart; this causes a common performance decrease and a formidable computational cost increase of traditional approaches. Novel methodologies are therefore needed to characterize data in high dimensional spaces.
Considering the parsimonious degrees of freedom of high dimensional data compared to its dimensionality, we study the union-of-subspaces (UoS) model, as a generalization of the linear subspace model. The UoS model preserves the simplicity of the linear subspace model, and enjoys the additional ability to address nonlinear data. We show a sufficient condition to use l1 minimization to reveal the underlying UoS structure, and further propose a bi-sparsity model (RoSure) as an effective algorithm, to recover the given data characterized by the UoS model from errors/corruptions.
As an interesting twist on the related problem of Dictionary Learning Problem, we discuss the sparse null space problem (SNS). Based on linear equality constraint, it first appeared in 1986 and has since inspired results, such as sparse basis pursuit, we investigate its relation to the analysis dictionary learning problem, and show that the SNS problem plays a central role, and may naturally be exploited to solve dictionary learning problems.
Substantiating examples are provided, and the application and performance of these approaches are demonstrated on a wide range of problems, such as face clustering and video segmentation.
Biography: Hamid Krim (F) received his degrees in Electrical Engineering. As a member of technical staff at AT&T Bell Labs, he has worked in the area of telephony and digital communication systems/subsystems. In 1991, he became a NSF Post-doctoral scholar at Foreign Centers of Excellence (LSS Supelec/Univ. of Orsay, Paris, France). In 1992, he joined the Laboratory for Information and Decision Systems, MIT, Cambridge, MA, as a Research Scientist performing/supervising research in his area of interest. In 1998, he joined the Electrical and Computer Engineering Department at North Carolina State University, Raleigh, N.C., where he is currently Professor and directing the Vision, Information, Statistical Signal Theories and Applications (VISSTA) Laboratory.
Dr. Krim’s editorial activities include: Editorial Board Member, IEEE Transactions on Signal Processing (2002-2004); Editorial Board Member, IEEE Signal Processing Magazine (2014).
Dr. Krim is an IEEE Fellow and was a Fellow, Japanese Foundation for the Advancement of Research in Science and Engineering at the University of Tokyo, Japan. Dr. Krim is a Member of SIAM and of Sigma Xi. He is an original contributor and now an Affiliate of the Center for Imaging Science, sponsored by the Army. He is a recipient, NSF Career Young Investigator Award.
Dr. Krim’s research interests are in statistical signal processing and mathematical modeling with a keen emphasis on applications. He has been particularly interested in introducing geometric and topological tools to statistical signal processing problems and applications. His research has primarily centered on estimation theoretic problems and modeling. Dr. Krim has published extensively on these areas with an impact amounting to over 5000 citations to date.