By Topic

Anomaly Preserving \ell _{\scriptscriptstyle 2,\infty } -Optimal Dimensionality Reduction Over a Grassmann Manifold

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Kuybeda, O. ; Dept. of Electr. Eng., Technion - Israel Inst. of Technol., Haifa, Israel ; Malah, D. ; Barzohar, M.

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.

Published in:

Signal Processing, IEEE Transactions on  (Volume:58 ,  Issue: 2 )