Fast Principal Component Extraction Using Givens Rotations

In this letter, we elaborate a new version of the orthogonal projection approximation and subspace tracking (OPAST) for the extraction and tracking of the principal eigenvectors of a positive Hermitian covariance matrix. The proposed algorithm referred to as principal component OPAST (PC-OPAST) esti...

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Bibliographic Details
Published in:IEEE signal processing letters 2008, Vol.15, p.369-372
Main Authors: Bartelmaos, S., Abed-Meraim, K.
Format: Article
Language:English
Subjects:
Adaptive algorithm
Covariance matrix
Data mining
Fast adaptive algorithms
Feature extraction
Givens rotations
Information analysis
Matrices
Matrix decomposition
Principal component analysis
principal component analysis (PCA)
Signal processing algorithms
Singular value decomposition
Studies
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Summary:In this letter, we elaborate a new version of the orthogonal projection approximation and subspace tracking (OPAST) for the extraction and tracking of the principal eigenvectors of a positive Hermitian covariance matrix. The proposed algorithm referred to as principal component OPAST (PC-OPAST) estimates the principal eigenvectors (not only a random basis of the principal subspace as for OPAST) of the considered covariance matrix. Also, it guarantees the orthogonality of the weight matrix at each iteration and requires flops per iteration, where is the size of the observation vector and is the number of eigenvectors to estimate. (The number of flops per iteration represents the total number of multiplication, division, and square root operations that are required to extract the desired eigenvectors at each iteration.) The estimation accuracy and tracking properties of PC-OPAST are illustrated through simulation results and compared with the well-known singular value decomposition (SVD) method and other recently proposed PCA algorithms.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2008.920006