Using conditional bias in principal component analysis for the evaluation of joint influence on the eigenvalues of the covariance matrix

Enguix-González, Alicia; Muñoz, Juan Manuel; Rebollo, Juan Luis Moreno; Barranco-Chamorro, I.

doi:10.1016/j.amc.2012.02.054

Cited by 2 publications

(4 citation statements)

References 28 publications

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“…The conditional bias of an eigenvalue has already been tackled in Enguix-González et al [1] to detect influential observations in Principal Component Analysis. The conditional bias of an eigenvector will be dealt with in a paper in the near future.…”

Section: Discussionmentioning

confidence: 99%

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A better approximation of moments of the eigenvalues and eigenvectors of the sample covariance matrix

Enguix-González

Rebollo

Muñoz

2015

Journal of Multivariate Analysis

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a b s t r a c tLawley (Lawley, 1956) obtained an approximation, through the first terms of a series expansion, of certain moments of an eigenvalue of the sample covariance matrix. The aim of this paper is to improve that approximation and to calculate a similar approximation for certain moments of the associated eigenvector. The results have practical applications in certain fields of Statistics, such as Influence Analysis.

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Section: Discussionmentioning

confidence: 99%

“…Analogously, a series expansion for  λ k can be obtained by replacing α k ( ) by λ k ( ) in (2). Note that the first terms of the series expansion are given in (1).…”

Section: Series Expansion Of Eigenvalues and Eigenvectorsmentioning

confidence: 98%

A better approximation of moments of the eigenvalues and eigenvectors of the sample covariance matrix

Enguix-González

Rebollo

Muñoz

2015

Journal of Multivariate Analysis

Self Cite

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“…The larger the value on the diagonal line of the matrix, the variables are more important. Conversely, the smaller the value, the smaller the corresponding variable is the secondary variable of the noise signal [15][16][17].…”

Section: Algorithm Derivation Of Pca Extraction Model Of Processing Roller's Performance Degradation Featurementioning

confidence: 99%

“…In equation (15), the relationship between the orthogonal matrix R and rotating orthogonal matrix R ðkÞ pq ðθÞ of equation ( 13) is R = R In order to better screen eigenvalues of covariance matrix C Z , it is necessary to calculate the cumulative contribution rate of eigenvalues. Let λ i denote eigenvalue of covariance matrix C Z , the cumulative sum of the first eigenvalues is ∑ l i=1 λ i , and cumulative sum of all eigenvalues is ∑ m i=1 λ i , l < m. Then, the principal component value (or variance ratio) of single eigenvalue is calculated by λ i /∑ m i=1 λ i .…”

Section: International Journal Of Rotating Machinerymentioning

confidence: 99%

Research on Feature Extraction of Performance Degradation for Flexible Material R2R Processing Roller Based on PCA

Deng

Zhou

Yao

et al. 2020

International Journal of Rotating Machinery

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Performance feature extraction is the primary problem in equipment performance degradation assessment. To handle the problem of high-dimensional performance characterization and complexity of calculating the performance indicators in flexible material roll-to-roll processing, this paper proposes a PCA method for extracting the degradation characteristic of roll shaft. Based on the analysis of the performance influencing factors of flexible material roll-to-roll processing roller, a principal component analysis extraction model was constructed. The original feature parameter matrix composed of 10-dimensional feature parameters such as time domain, frequency domain, and time-frequency domain vibration signal of the roll shaft was established; then, we obtained a new feature parameter matrix Z org ∗ by normalizing the original feature parameter matrix. The correlation measure between every two parameters in the matrix Z org ∗ was used as the eigenvalue to establish the covariance matrix of the performance degradation feature parameters. The Jacobi iteration method was introduced to derive the algorithm for solving eigenvalue and eigenvector of the covariance matrix. Finally, using the eigenvalue cumulative contribution rate as the screening rule, we linearly weighted and fused the eigenvectors and derived the feature principal component matrix F of the processing roller vibration signal. Experiments showed that the initially obtained, 10-dimensional features of the processing rollers’ vibration signals, such as average, root mean square, kurtosis index, centroid frequency, root mean square of frequency, standard deviation of frequency, and energy of the intrinsic mode function component, can be expressed by 3-dimensional principal components F 1 , F 2 , and F 3 . The vibration signal features reduction dimension was realized, and F 1 , F 2 , and F 3 contain 98.9% of the original vibration signal data, further illustrating that the method has high precision in feature parameters’ extraction and the advantage of eliminating the correlation between feature parameters and reducing the workload selecting feature parameters.

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Using conditional bias in principal component analysis for the evaluation of joint influence on the eigenvalues of the covariance matrix

Cited by 2 publications

References 28 publications

A better approximation of moments of the eigenvalues and eigenvectors of the sample covariance matrix

A better approximation of moments of the eigenvalues and eigenvectors of the sample covariance matrix

Research on Feature Extraction of Performance Degradation for Flexible Material R2R Processing Roller Based on PCA

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