DocumentCode :
1448416
Title :
Anomaly Preserving \\ell _{\\scriptscriptstyle 2,\\infty } -Optimal Dimensionality Reduction Over a Grassmann Manifold
Author :
Kuybeda, Oleg ; Malah, David ; Barzohar, Meir
Author_Institution :
Dept. of Electr. Eng., Technion - Israel Inst. of Technol., Haifa, Israel
Volume :
58
Issue :
2
fYear :
2010
Firstpage :
544
Lastpage :
552
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 l2-norm of the signal as compared to the noise, l2 -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 l2-norms, denoted as l2,l and designed to represent well both abundant and anomaly measurements. However, the MX-SVD algorithm is greedy and only approximately minimizes the proposed l2,l-norm of the residuals. In this paper we develop an optimal algorithm for the minization of the l2,l-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 n dimensional subspaces in IRm, mn, which is a Grassmann manifold. The results of applying MOOSE, MX-SVD, and l2- based approaches are demonstrated both on simulated and real hyperspectral data.
Keywords :
conjugate gradient methods; estimation theory; signal processing; singular value decomposition; Grassmann manifold; HySime; MOCA; MOOSE; MX-SVD algorithm; anomaly data vectors; anomaly detection; anomaly measurements; anomaly preserving l 2,l-optimal dimensionality reduction; anomaly rare vectors; data misrepresentation residuals; data-residual l2-norms; high-dimensional noisy signals; hyperspectral images; hyperspectral signal identification by minimum error; maximum orthogonal complements analysis; maximum orthogonal complements optimal subspace estimation; min-max-SVD; natural conjugate gradient learning approach; real hyperspectral data; redundancy reduction; signal subspace rank; signal-subspace estimation; singular value decomposition; Anomaly detection; Grassmann manifold; Min-Max-SVD (MX-SVD); dimensionality reduction; hyperspectral images; hyperspectral signal identification by minimum error (HySime); maximum orthogonal-complements analysis (MOCA); redundancy reduction; signal-subspace rank; singular value decomposition (SVD);
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/TSP.2009.2032580
Filename :
5256322
Link To Document :
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