Improving Subspace Segmentation with the Rayleigh Quotient
Shankar Rao, Andrew Wagner, Allen Y. Yang, Yi Ma · Illinois Digital Environment for Access to Learning and Scholarship (University of Illinois at Urbana-Champaign) · 2005
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.