2008
DOI: 10.1007/s11063-007-9069-2
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New Routes from Minimal Approximation Error to Principal Components

Abstract: Abstract. We introduce two new methods of deriving the classical PCA in the framework of minimizing the mean square error upon performing a lower-dimensional approximation of the data. These methods are based on two forms of the mean square error function. One of the novelties of the presented methods is that the commonly employed process of subtraction of the mean of the data becomes part of the solution of the optimization problem and not a pre-analysis heuristic. We also derive the optimal basis and the min… Show more

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Cited by 104 publications
(64 citation statements)
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“…types of oil wells were determined Fig.1 Flow chart of cluster analysis Principal component analysis and cluster analysis were the key parts of the whole process [13] . First, by linear combination, the original multiple indicatiors had become a few independent indicators that fully reflected the overall information, so as to make further analysis [14] . Second, the main factors that caused oil wells corrosion and scaling were determined by removing the dependent variable.…”
Section: Clustering Analysis Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…types of oil wells were determined Fig.1 Flow chart of cluster analysis Principal component analysis and cluster analysis were the key parts of the whole process [13] . First, by linear combination, the original multiple indicatiors had become a few independent indicators that fully reflected the overall information, so as to make further analysis [14] . Second, the main factors that caused oil wells corrosion and scaling were determined by removing the dependent variable.…”
Section: Clustering Analysis Methodsmentioning
confidence: 99%
“…Principal components were selected according to the order of contribution rate of different components, then the selected principal components were as weights for linear weighting [14] . They were sorted according to the score value [16] .…”
Section: Principal Component Analysis Of Water Quality Datamentioning
confidence: 99%
“…(1) are difficult to determine quantitatively. In this subsection we employ principal component analysis [6] to reconstruct the Eq. (1).…”
Section: Principal Component Analysis Using Covariance Methodsmentioning
confidence: 99%
“…φ r $. This formulation is common in Principal Component Analysis [37,38,39] where it is introduced in the framework of variance maximization or minimal error of the approximation matrixX [40,41,42].…”
Section: Pod Decomposition Of Piv Image Recordingsmentioning
confidence: 99%