Paper Info
Title
Anomaly Preserving L(2,Infinity)-Optimal Dimensionality Reduction Over A Grassmann Manifold
Abstract
In this paper, we address the problem of redundancy reduction of high-dimensional noisy signals that may contain anomaly (rare) vectors, which we wish to preserve. Since anomaly data vectors contribute weakly to the l(2)-norm of the signal as compared to the noise, l(2)-based criteria are unsatisfactory for obtaining a good representation of these vectors. As a remedy, a new approach, named Min-Max-SVD (MX-SVD) was recently proposed for signal-subspace estimation by attempting to minimize the maximum of data-residual l(2,infinity)-norms, denoted as l(2,infinity) and designed to represent well both abundant and anomaly measurements. However, the MX-SVD algorithm is greedy and only approximately minimizes the proposed l(2,infinity)-norm of the residuals. In this paper we develop an optimal algorithm for the minization of the l(2,infinity)-norm of data misrepresentation residuals, which we call Maximum Orthogonal complements Optimal Subspace Estimation (MOOSE). The optimization is performed via a natural conjugate gradient learning approach carried out on the set of dimensional subspaces in R-m, > n, which is a Grassmann manifold. The results of applying MOOSE, MX-SVD, and l(2)-based approaches are demonstrated both on simulated and real hyperspectral data.
Year
DOI
Venue
2010
10.1109/TSP.2009.2032580
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Keywords
DocType
Volume
Anomaly detection, dimensionality reduction, Grassmann manifold, hyperspectral images, hyperspectral signal identification by minimum error (HySime), maximum orthogonal-complements analysis (MOCA), Min-Max-SVD (MX-SVD), redundancy reduction, signal-subspace rank, singular value decomposition (SVD)
Journal
58
Issue
ISSN
Citations 
2
1053-587X
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Oleg Kuybeda131.20
David Malah221960.95
Meir Barzohar39411.06