University of Illinois Urbana-Champaign

Improving Subspace Segmentation with the Rayleigh Quotient

Rao, Shankar R.; Wagner, Andrew W.; Yang, Allen Y.; Ma, Yi

Content Files
UILU-ENG-05-2206_DC-216 assembled.pdf

Permalink

https://hdl.handle.net/2142/99592

Description

Title
Improving Subspace Segmentation with the Rayleigh Quotient
Author(s)
  • Rao, Shankar R.
  • Wagner, Andrew W.
  • Yang, Allen Y.
  • Ma, Yi
Issue Date
2005-04
Keyword(s)
  • Subspace
  • Polynomial
  • Segmentation
  • Clustering
  • GPCA
  • Rayleigh
  • Robust
  • Discriminant
  • Fisher
Date of Ingest
2018-04-03T19:30:31Z
Abstract
In this paper, we investigate the problem of subspace segmentation in the presence of significant noise. We draw upon multivariate discriminating statistics to improve the algebraic Generalized Principal Component Analysis method with the notion of Segmentation Polynomials. A Segmentation Polynomial is a polynomial that both fits the data well and also provides the best segmentation of noisy samples drawn from different linear subspaces. We obtain Segmentation Polynomials by minimizing a ratio that is remarkably similar to the Rayleigh Quotient used in Fisher’s Linear Discriminant. We will show that using a single Segmentation Polynomial, one can robustly segment data samples into linear subspaces in the presence of significant noise. We evaluate the performance of our method on highly noisy samples, and demonstrate its use in piece-wise linear fitting of nonlinear manifolds, segmenting color images, detection of straight lines in images, and sparse image representation.
Publisher
Coordinated Science Laboratory, University of Illinois at Urbana-Champaign
Series/Report Name or Number
Coordinated Science Laboratory Report no. UILU-ENG-05-2206, DC-216
Type of Resource
text
Genre of Resource
Technical Report
Language
en
Permalink
http://hdl.handle.net/2142/99592
Sponsor(s)/Grant Number(s)
NSF

Owning Collections

Report - Coordinated Science Laboratory PRIMARY