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Nature Reviews Methods Primers, 2022
Principal component analysis is a versatile statistical method for reducing a cases-byvariables data table to its essential features, called principal components. Principal components are a few linear combinations of the original variables that maximally explain the variance of all the variables.
Michael Greenacre +5 more
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Principal component analysis is a versatile statistical method for reducing a cases-byvariables data table to its essential features, called principal components. Principal components are a few linear combinations of the original variables that maximally explain the variance of all the variables.
Michael Greenacre +5 more
openaire +5 more sources
Transfusion, 2018
A brief introduction to principal component analysis is provided, with applications in sample discrimination and in the development of inverse calibration models using full spectral information.
Aaron S. Hess, John R. Hess
+9 more sources
A brief introduction to principal component analysis is provided, with applications in sample discrimination and in the development of inverse calibration models using full spectral information.
Aaron S. Hess, John R. Hess
+9 more sources
WIREs Computational Statistics, 2010
Principal Component Analysis (PCA, [24, 25]) is a technique which, quite literally, takes a di_erent viewpoint of multivariate data. In fact, PCA de_nes new variables, consisting of linear combinations of the original ones, in such a way that the _rst axis is in the direction containing most variation.
Aiyi Liu, Enrique F. Schisterman
+7 more sources
Principal Component Analysis (PCA, [24, 25]) is a technique which, quite literally, takes a di_erent viewpoint of multivariate data. In fact, PCA de_nes new variables, consisting of linear combinations of the original ones, in such a way that the _rst axis is in the direction containing most variation.
Aiyi Liu, Enrique F. Schisterman
+7 more sources
2003
Chapter 9 presented the basic geometric tools needed to produce a lower dimensional description of the rows and columns of a multivariate data matrix. Principal components analysis has the same objective with the exception that the rows of the data matrix \({{\mathcal{X}}}\) will now be considered as observations from a p-variate random variable X. The
Léopold Simar, Wolfgang Karl Härdle
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Chapter 9 presented the basic geometric tools needed to produce a lower dimensional description of the rows and columns of a multivariate data matrix. Principal components analysis has the same objective with the exception that the rows of the data matrix \({{\mathcal{X}}}\) will now be considered as observations from a p-variate random variable X. The
Léopold Simar, Wolfgang Karl Härdle
openaire +2 more sources
2012
Principal components analysis (PCA) is a standard tool in multivariate data analysis to reduce the number of dimensions, while retaining as much as possible of the data's variation. Instead of investigating thousands of original variables, the first few components containing the majority of the data's variation are explored.
Stefanie Hartmann +3 more
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Principal components analysis (PCA) is a standard tool in multivariate data analysis to reduce the number of dimensions, while retaining as much as possible of the data's variation. Instead of investigating thousands of original variables, the first few components containing the majority of the data's variation are explored.
Stefanie Hartmann +3 more
openaire +2 more sources
2005
One of the problems with a lot of sets of multivariate data is that there are simply too many variables to make the application of the graphical techniques described in the previous chapters successful in providing an informative initial assessment of the data. And having too many variables can also cause problems for other multivariate techniques that
Brian Everitt, Torsten Hothorn
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One of the problems with a lot of sets of multivariate data is that there are simply too many variables to make the application of the graphical techniques described in the previous chapters successful in providing an informative initial assessment of the data. And having too many variables can also cause problems for other multivariate techniques that
Brian Everitt, Torsten Hothorn
openaire +2 more sources
Coupled Principal Component Analysis
IEEE Transactions on Neural Networks, 2004A framework for a class of coupled principal component learning rules is presented. In coupled rules, eigenvectors and eigenvalues of a covariance matrix are simultaneously estimated in coupled equations. Coupled rules can mitigate the stability-speed problem affecting noncoupled learning rules, since the convergence speed in all eigendirections of the
Möller, Ralf, Könies, Axel
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Principal Component Analysis [PDF]
, 2012 Among linear DR methods, principal component analysis (PCA) perhaps is the most important one. In linear DR, the dissimilarity of two points in a data set is defined by the Euclidean distance between them, and correspondingly, the similarity is described by their inner product.
Panos M. Pardalos +3 more
openaire +3 more sources
2011
This chapter explains the theory of Principal component analysis (PCA) in detail and presents practical implementation issues along with various application examples. It introduces the mathematical concepts behind PCA such as mean value, covariance, eigenvalues, and eigenvectors. The principal components are ordered in way that the principal components
Anastasios Tefas, Ioannis Pitas
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This chapter explains the theory of Principal component analysis (PCA) in detail and presents practical implementation issues along with various application examples. It introduces the mathematical concepts behind PCA such as mean value, covariance, eigenvalues, and eigenvectors. The principal components are ordered in way that the principal components
Anastasios Tefas, Ioannis Pitas
openaire +2 more sources
2013
Most signal-processing problems can be reduced to some form of eigenvalue or singular-value problems.
M. N. S. Swamy, Ke-Lin Du
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Most signal-processing problems can be reduced to some form of eigenvalue or singular-value problems.
M. N. S. Swamy, Ke-Lin Du
openaire +2 more sources