TY - JOUR
T1 - Online Dominant Generalized Eigenvectors Extraction via a Randomized Algorithm
AU - Cai, Haoyuan
AU - Kaloorazi, Maboud
AU - Chen, Jie
AU - Chen, Wei
AU - Richard, Cedric
N1 - Publisher Copyright:
© 1967-2012 IEEE.
PY - 2023/6/1
Y1 - 2023/6/1
N2 - This paper is concerned with online algorithms for the generalized Hermitian eigenvalue problem (GHEP). We first present an algorithm based on randomization, termed alternate-projections randomized eigenvalue decomposition (APR-EVD), to solve the standard eigenvalue problem. The APR-EVD algorithm is computationally efficient and can be computed by making only one pass through the input matrix. We then develop two online algorithms based on APR-EVD for the dominant generalized eigenvectors extraction. Our proposed algorithms use the fact that GHEP is transformed into a standard eigenvalue problem, however to avert computations of a matrix inverse and inverse of the square root of a matrix, which are prohibitive, they exploit the rank-1 strategy for the transformation. Our algorithms are devised for extracting generalized eigenvectors for scenarios in which observed stochastic signals have unknown covariance matrices. The effectiveness and practical applicability of our proposed algorithms are validated through numerical experiments with synthetic and real-world data.
AB - This paper is concerned with online algorithms for the generalized Hermitian eigenvalue problem (GHEP). We first present an algorithm based on randomization, termed alternate-projections randomized eigenvalue decomposition (APR-EVD), to solve the standard eigenvalue problem. The APR-EVD algorithm is computationally efficient and can be computed by making only one pass through the input matrix. We then develop two online algorithms based on APR-EVD for the dominant generalized eigenvectors extraction. Our proposed algorithms use the fact that GHEP is transformed into a standard eigenvalue problem, however to avert computations of a matrix inverse and inverse of the square root of a matrix, which are prohibitive, they exploit the rank-1 strategy for the transformation. Our algorithms are devised for extracting generalized eigenvectors for scenarios in which observed stochastic signals have unknown covariance matrices. The effectiveness and practical applicability of our proposed algorithms are validated through numerical experiments with synthetic and real-world data.
KW - Dominant generalized eigenvector extraction
KW - fast subspace estimation and tracking
KW - matrix decomposition
KW - online algorithms
KW - Randomized algorithms
KW - real-time hyperspectral image denoising
UR - http://www.scopus.com/inward/record.url?scp=85149369520&partnerID=8YFLogxK
U2 - 10.1109/TVT.2023.3243244
DO - 10.1109/TVT.2023.3243244
M3 - 文章
AN - SCOPUS:85149369520
SN - 0018-9545
VL - 72
SP - 7597
EP - 7612
JO - IEEE Transactions on Vehicular Technology
JF - IEEE Transactions on Vehicular Technology
IS - 6
ER -