On a Class of Orthonormal Algorithms for Principal and Minor Subspace Tracking |
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Authors: | K. Abed-Meraim A. Chkeif Y. Hua S. Attallah |
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Affiliation: | (1) TSI Department, Telecom Paris, 46, rue Barrault, 75634 Paris Cedex 13, France;(2) Department of Electrical Engineering, University of California, Riverside, 92521, CA, USA;(3) School of Electrical & Computer Engineering, Curtin University of Technology, GPO Box U1987, Perth, 6845, Australia |
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Abstract: | This paper elaborates on a new class of orthonormal power-based algorithms for fast estimation and tracking of the principal or minor subspace of a vector sequence. The proposed algorithms are closely related to the natural power method that has the fastest convergence rate among many power-based methods such as the Oja method, the projection approximation subspace tracking (PAST) method, and the novel information criterion (NIC) method. A common feature of the proposed algorithms is the exact orthonormality of the weight matrix at each iteration. The orthonormality is implemented in a most efficient way. Besides the property of orthonormality, the new algorithms offer, as compared to other power based algorithms, a better numerical stability and a linear computational complexity. |
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Keywords: | adaptive algorithm orthonormality principal & minor component analysis subspace tracking |
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