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Title:Estimation of Subspace Arrangements with Applications in Modeling and Segmenting Mixed Data
Author(s):Ma, Yi; Yang, Allen Y.; Derksen, Harm; Fossum, Robert
Subject(s):Subspace arrangement
Hilbert function
Generalized principal component analysis
Model selection
Outlier detection
Abstract:In recent years, subspace arrangements have become an increasingly popular class of mathematical objects to be used for modeling a multivariate mixed data set that is (approximately) piecewise linear. A subspace arrangement is a union of multiple subspaces. Each subspace can be conveniently used to model a homogeneous subset of the data. Hence, all the subspaces together can capture the heterogeneous structures within the data set. In this paper, we give a comprehensive introduction to one new approach for the estimation of subspace arrangements, known as generalized principal component analysis. We provide a comprehensive summary of important algebraic properties and statistical facts that are crucial for making the inference of subspace arrangements both efficient and robust, even when the given data are corrupted with noise or contaminated by outliers. This new method in many ways improves and generalizes extant methods for modeling or clustering mixed data. There have been successful applications of this new method to many real-world problems in computer vision, image processing, and system identification. In this paper, we will examine a couple of those representative applications.
Issue Date:2006-04
Publisher:Coordinated Science Laboratory, University of Illinois at Urbana-Champaign
Series/Report:Coordinated Science Laboratory Report no. UILU-ENG-06-2202, DC-221
Genre:Technical Report
Sponsor:National Science Foundation / NSF CAREER IIS-0347456, NSF CRS-EHS-0509151, NSF CCF-TF-0514955, and NSF CAREER DMS-034901
ONR YIP N00014-05-1-0633
Date Available in IDEALS:2018-04-03

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