Subspace algorithms for the stochastic identification problem
Automatica (Journal of IFAC)
Subspace-based methods for the identification of linear time-invariant systems
Automatica (Journal of IFAC) - Special issue on trends in system identification
The Geometry of Algorithms with Orthogonality Constraints
SIAM Journal on Matrix Analysis and Applications
Matrix algorithms
Convex Optimization
Signal subspace identification in hyperspectral linear mixtures
IbPRIA'05 Proceedings of the Second Iberian conference on Pattern Recognition and Image Analysis - Volume Part II
A least-squares approach to blind channel identification
IEEE Transactions on Signal Processing
Subspace methods for the blind identification of multichannel FIRfilters
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
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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,∞ and designed to represent well both abundant and anomaly measurements. However, the MX-SVD algorithm is greedy and only approximately minimizes the proposed l2,∞-norm of the residuals. In this paper we develop an optimal algorithm for the minization of the l2,∞-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 IRm,m n, 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.