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Title:Hilbert Functions and Applications to the Estimation of Subspace Arrangements
Author(s):Yang, Allen Y.; Rao, Shankar; Wagner, Andrew; Ma, Yi; Fossum, Robert M.
Subject(s):Subspace segmentation
Hilbert function
Subspace arrangement
Model selection
Affine projection
Motion segmentation
Abstract:This paper develops a new mathematical framework for studying the subspace-segmentation problem. We examine some important algebraic properties of subspace arrangements that are closely related to the subspace-segmentation problem. More specifically, we introduce an important class of invariants given by the Hilbert functions. We show that there exist rich relations between subspace arrangements and their corresponding Hilbert functions. We propose a new subspace- segmentation algorithm, and showcase two applications to demonstrate how the new theoretical revelation may solve subspace segmentation and model selection problems under less restrictive conditions with improved results.
Issue Date:2005-07
Publisher:Coordinated Science Laboratory, University of Illinois at Urbana-Champaign
Series/Report:Coordinated Science Laboratory Report no. UILU-ENG-05-2213, DC-217
Genre:Technical Report
Sponsor:National Science Foundation / CAREER IIS-0347456, CRS-EHS-0509151, and CCF-TF-0514955
ONR YIP N00014-05-1-0633
Date Available in IDEALS:2018-04-03

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