Online Dominant Generalized Eigenvectors Extraction via a Randomized Algorithm

Haoyuan Cai, Maboud Kaloorazi, Jie Chen, Wei Chen, Cedric Richard

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)7597-7612
Number of pages16
JournalIEEE Transactions on Vehicular Technology
Volume72
Issue number6
DOIs
StatePublished - 1 Jun 2023

Keywords

  • Dominant generalized eigenvector extraction
  • fast subspace estimation and tracking
  • matrix decomposition
  • online algorithms
  • Randomized algorithms
  • real-time hyperspectral image denoising

Fingerprint

Dive into the research topics of 'Online Dominant Generalized Eigenvectors Extraction via a Randomized Algorithm'. Together they form a unique fingerprint.

Cite this