Analysis of a class of continuous-time algorithms for principal component analysis and subspace tracking

Author

Dehaene, Jeroen ; Moonen, Marc ; Vandewalle, Joos

Author_Institution

ESAT, Katholieke Univ., Leuven, Heverlee, Belgium

Volume

46

Issue

3

fYear

1999

fDate

3/1/1999 12:00:00 AM

Firstpage

364

Lastpage

372

Abstract

We give a new analysis of a class of continuous-time subspace tracking algorithms, related to a number of discrete-time algorithms, such as stochastic gradient algorithms, spherical subspace trackers, and a new discrete-time algorithm based on one of the continuous-time algorithms. Using formulas for tracking the singular value decomposition (SVD) of a time-varying matrix, we show attraction to orthogonality of the matrix representing the subspace estimate, and we analyze the evolution of the canonical angles between the subspace estimate and the subspace to be estimated

Keywords

adaptive signal processing; principal component analysis; singular value decomposition; tracking; SVD; continuous-time algorithms; discrete-time algorithm; principal component analysis; singular value decomposition; subspace estimate; subspace tracking; time-varying matrix; Algorithm design and analysis; Eigenvalues and eigenfunctions; Estimation theory; Independent component analysis; Matrix decomposition; Principal component analysis; Signal analysis; Signal processing algorithms; Singular value decomposition; Stochastic processes;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.751309

Filename

751309