The Modified Increment Method for Eigenspace Model

Academic Journal of Applied Mathematical Sciences ◽

10.32861/ajams.74.187.191 ◽

2021 ◽

pp. 187-191

Author(s):

Chunjie Wei ◽

Jian Wang

Keyword(s):

Big Data ◽

Numerical Analysis ◽

Covariance Matrix ◽

Sample Covariance Matrix ◽

Storage Space ◽

Computational Costs ◽

Incremental Method ◽

Sample Covariance ◽

And Storage

Eigenspace is a convenient way to represent sets of observations with widespread applications, so it is necessary to accurately calculate the eigenspace of data. With the advent of the era of big data, the increasing and updating of data bring great challenges to the solution of eigenspace. Hall, et al. [1], proposed that the incremental method could update the eigenspace of data online, which reduces computational costs and storage space. In this paper, the updating coefficient of the sample covariance matrix in an incremental method is modified. Numerical analysis shows that the modified updating form has better performance.

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Asymptotic Distributions of Functions of the Eigenvalues of the Sample Covariance Matrix and Canonical Correlation Matrix in Multivariate Time Series

10.21236/ada170282 ◽

1986 ◽

Author(s):

M. Taniguchi ◽

P. R. Krishnaiah

Keyword(s):

Time Series ◽

Covariance Matrix ◽

Canonical Correlation ◽

Correlation Matrix ◽

Multivariate Time Series ◽

Asymptotic Distributions ◽

Sample Covariance Matrix ◽

Sample Covariance

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Analysis of grid operation state based on improved maximum eigenvalue sample covariance matrix algorithm

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1177/09596518211001270 ◽

2021 ◽

pp. 095965182110012

Author(s):

Dinghui Wu ◽

Juan Zhang ◽

Bo Wang ◽

Tinglong Pan

Keyword(s):

Covariance Matrix ◽

Signal To Noise Ratio ◽

Poor Performance ◽

Sample Covariance Matrix ◽

Maximum Eigenvalue ◽

Signal To Noise ◽

Matrix Algorithm ◽

Sample Covariance ◽

Noise Ratio ◽

Application Fields

Traditional static threshold–based state analysis methods can be applied to specific signal-to-noise ratio situations but may present poor performance in the presence of large sizes and complexity of power system. In this article, an improved maximum eigenvalue sample covariance matrix algorithm is proposed, where a Marchenko–Pastur law–based dynamic threshold is introduced by taking all the eigenvalues exceeding the supremum into account for different signal-to-noise ratio situations, to improve the calculation efficiency and widen the application fields of existing methods. The comparison analysis based on IEEE 39-Bus system shows that the proposed algorithm outperforms the existing solutions in terms of calculation speed, anti-interference ability, and universality to different signal-to-noise ratio situations.

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