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) 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.