• Corpus ID: 17086438

An Amendment of Fast Subspace Tracking Methods

@article{Cheng2011AnAO,
  title={An Amendment of Fast Subspace Tracking Methods},
  author={Zhu Cheng and Zhan Wang and Haitao Liu and Majid Ahmadi},
  journal={arXiv: Numerical Analysis},
  year={2011}
}
Tuning stepsize between convergence rate and steady state error level or stability is a problem in some subspace tracking schemes. Methods in DPM and OJA class may show sparks in their steady state error sometimes, even with a rather small stepsize. By a study on the schemes' updating formula, it is found that the update only happens in a specific plane but not all the subspace basis. Through an analysis on relationship between the vectors in that plane, an amendment as needed is made on the… 
View PDF on arXiv

Figures from this paper

References

SHOWING 1-10 OF 24 REFERENCES
Modification Algorithms for a Class of Subspace Tracking Methods
TLDR
Modified methods for subspace tracking methods are proposed, named as MFDPM and MFOOJA, which are numerically stable and less computational complexity and guarantee orthonormality convergence.
Fast and Stable Subspace Tracking
TLDR
This work develops a fast and numerically robust implementation of DPM, which comes at a considerably lower computational cost, and constitutes the first numerically stable, low complexity, algorithm for tracking subspaces corresponding to the smallest singular values.
Principal and Minor Subspace Tracking: Algorithms & Stability Analysis
  • S. Bartelmaos, K. Abed-Meraim
  • Computer Science
    2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings
  • 2006
TLDR
A fast and numerically robust implementation of Oja algorithm (FOOja: fast orthogonal Oja) is proposed, which guarantees the orthogonality of the weight matrix at each iteration.
Adaptive eigensubspace algorithms for direction or frequency estimation and tracking
  • J. Yang, Mostafa Kave
  • Engineering, Computer Science
    IEEE Trans. Acoust. Speech Signal Process.
  • 1988
TLDR
The authors present an adaptive estimator of the complete noise or signal subspace of a sample covariance matrix as well as the estimator's practical implementations and simulation results show that the adaptive subspace algorithms perform substantially better than P.A. Thompson's (1980) adaptive version of V.F. Pisarenko's technique in estimating frequencies or directions of arrival (DOA) of plane waves.
Subspace estimation and tracking using enhanced versions of Oja's algorithm
  • S. Attallah, K. Abed-Meraim
  • Computer Science
    2001 IEEE Third Workshop on Signal Processing Advances in Wireless Communications (SPAWC'01). Workshop Proceedings (Cat. No.01EX471)
  • 2001
TLDR
Two normalized versions of the Oja (1992) algorithm are presented which can be used for the estimation of minor and principal subspaces of a vector sequence and offer a faster convergence, better orthogonality and numerical stability with a slight increase in computational complexity.
A Novel Orthonormalization Matrix Based Fast and Stable DPM Algorithm for Principal and Minor Subspace Tracking
TLDR
A fast and stable implementation of the DPM algorithm which has the merits of both the FRANS and FDPM approaches is investigated for principal and minor subspace tracking and reaches the 3np lower bound of the dominant complexity and guarantees the orthonormality of the tracked subspace.
Fast algorithms for subspace tracking
TLDR
Two normalized versions of Oja's (1992) algorithm (NOja and NOOja), which can be used for the estimation of minor and principal subspaces of a vector sequence, offer a faster convergence, orthogonality, and a better numerical stability.
Tracking a few extreme singular values and vectors in signal processing
TLDR
In various applications it is necessary to keep track of a low-rank approximation of a covariance matrix, R(t), slowly varying with time, and it is shown why this heavy computational burden is questionable in numerous situations and should be revised.
An analysis of the fast subspace tracking algorithm NOja
This paper analyses the fast subspace tracking algorithm recently proposed by Attallah and Abed-Meraim. Specifically, the associated Ordinary Differential Equation is derived and its properties…
Stable and Orthonormal OJA Algorithm With Low Complexity
TLDR
In this letter, a stable and orthonormal version of the OJA algorithm (SOOJA) is investigated for principal and minor subspace extraction and tracking and it obtains both a high numerical stability and a low computational complexity.
...
1
2
3
...