Estimation of Subspace Arrangements with Applications in Modeling and Segmenting Mixed Data

Ma, Yi; Yang, Allen Y.; Derksen, Harm; Fossum, Robert

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https://hdl.handle.net/2142/99595 Copy

Description

Title

Estimation of Subspace Arrangements with Applications in Modeling and Segmenting Mixed Data

Author(s)

• Ma, Yi
• Yang, Allen Y.
• Derksen, Harm
• Fossum, Robert

Issue Date

2006-04

Keyword(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.

Publisher

Coordinated Science Laboratory, University of Illinois at Urbana-Champaign

Series/Report Name or Number

Coordinated Science Laboratory Report no. UILU-ENG-06-2202, DC-221

Type of Resource

text

Language

en

Permalink

http://hdl.handle.net/2142/99595

Sponsor(s)/Grant Number(s)

• 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

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