Convexity, Sparsity, Nullity and all that… in Data Analysis

Monday March 7th, 2016 at 3:00 p.m. Prof. Hamid Krim, Department of Electrical & Computer Engineering of North Carolina State University, will be presenting a distinguished lecture, “Convexity, Sparsity, Nullity and all that… in Data Analysis”.

Speaker: Prof. Hamid Krim
Department of Electrical & Computer Engineering
North Carolina State University
Raleigh, NC, US

Day & Time: Monday, March 7th, 2016
3:00 p.m. – 4:00 p.m.

Location: Room VIC300, Ryerson University
285 Victoria St, Toronto
Map: https://goo.gl/maps/EAvPDLGSqrt

Contact: Mehrnaz Shokrollahi

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 stability 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 (R0Sure) 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 received his BSc., MSc. and PhD. in Electrical Engineering. He was a member of Technical staff at AT&T Bell Labs, where he has conducted R&D in the areas of telephony and digital communication systems/subsystems. Following an NSF post-doctoral fellowship at Foreign Centers of Excellence, LSS/University of Orsay, Paris, France. He later joined the Laboratory for Information and Decision Systems, MIT, Cambridge, MA as a Research Scientist, where he was performing and supervising research. He is presently Professor of Electrical Engineering in the ECE department, North Carolina State University, Raleigh, leading the Vision, Information and Statistical Signal Theories and Applications group. His research interests are in statistical signal and image analysis, and mathematical modelling, with a keen emphasis on applied problems in classification and recognition using geometric and topological tools. He is currently serving on the IEEE editorial board of SP, and the TCs of SPTM and Big Data Initiative, as well as an AE of the new IEEE Transactions on SP on Information Processing on Networks, and of the IEEE SP Magazine. He is also one of the 2015-2016 Distinguished Lecturers of the IEEE SP Society.