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【Academic Forum】Convexity, Sparsity, Nullity and all that … in Machine Learning

Source:Date:2017-03-28
 
Topic: Convexity, Sparsity, Nullity and all that … in Machine Learning
Lecturer: Hamid Krim, Professor of North Carolina State University,IEEE Fellow.
Host: Professor Ouyang Jiuquan, Associate Dean of Information Engineering Institute of Xiangtan University
Time: 2:00 pm ,March 30, 2017 
Venue: North Building of Engineering Building,201
 
Report Summary: 
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 thelinear 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 non-conforming 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 hassince 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.
Welcome all the teachers and students to participate!