Hilbert Functions and Applications to the Estimation of Subspace Arrangements

Yang, Allen Y.; Rao, Shankar; Wagner, Andrew; Ma, Yi; Fossum, Robert M.

Permalink

https://hdl.handle.net/2142/99593 Copy

Description

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.

Issue Date

2005-07

Keyword(s)

• Subspace segmentation
• GPCA
• 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.

Publisher

Coordinated Science Laboratory, University of Illinois at Urbana-Champaign

Series/Report Name or Number

Coordinated Science Laboratory Report no. UILU-ENG-05-2213, DC-217

Type of Resource

text

Language

en

Permalink

http://hdl.handle.net/2142/99593

Sponsor(s)/Grant Number(s)

• National Science Foundation / CAREER IIS-0347456, CRS-EHS-0509151, and CCF-TF-0514955
• ONR YIP N00014-05-1-0633

Owning Collections