Covariance-based Principal Components Analysis (PCA) Algorithm: Difference between revisions
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* (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Principal_component_analysis#Computing_PCA_using_the_covariance_method Retrieved:2019-10-14. | * (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Principal_component_analysis#Computing_PCA_using_the_covariance_method Retrieved:2019-10-14. | ||
** The following is a detailed description of PCA using the covariance method (see also [http://www.cs.otago.ac.nz/cosc453/student_tutorials/principal_components.pdf here]) as opposed to the correlation method. <P> | ** The following is a detailed description of PCA using the covariance method (see also [http://www.cs.otago.ac.nz/cosc453/student_tutorials/principal_components.pdf here]) as opposed to the correlation method. <P> The goal is to transform a given data set '''X''' of dimension ''p'' to an alternative data set '''Y''' of smaller dimension ''L''. Equivalently, we are seeking to find the matrix '''Y''', where '''Y''' is the [[Karhunen–Loève theorem|Karhunen–Loève]] transform (KLT) of matrix '''X''': : <math> \mathbf{Y} = \mathbb{KLT} \{ \mathbf{X} \} </math> | ||
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Latest revision as of 04:39, 18 August 2021
A Covariance-based Principal Components Analysis (PCA) Algorithm is a PCA algorithm by means of ...
- Context:
- It can be implemented by a Covariance-based PCA System.
- …
- Counter-Example(s):
- See: Covariance Matrix, Conjugate Transpose, Transpose, Bessel's Correction, Eigenvector, Diagonalizable Matrix, Diagonal Matrix, Eigenvalue.
References
2019
- (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Principal_component_analysis#Computing_PCA_using_the_covariance_method Retrieved:2019-10-14.
- The following is a detailed description of PCA using the covariance method (see also here) as opposed to the correlation method.
The goal is to transform a given data set X of dimension p to an alternative data set Y of smaller dimension L. Equivalently, we are seeking to find the matrix Y, where Y is the Karhunen–Loève transform (KLT) of matrix X: : [math]\displaystyle{ \mathbf{Y} = \mathbb{KLT} \{ \mathbf{X} \} }[/math]
- The following is a detailed description of PCA using the covariance method (see also here) as opposed to the correlation method.