Cross-Validatory Choice of the Number of Components From a Principal Component Analysis

A method is described for choosing the number of components to retain in a principal component analysis when the aim is dimensionality reduction. The correspondence between principal component analysis and the singular value decomposition of the data matrix is used. The method is based on successive...

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Bibliographic Details
Published in:Technometrics 1982-02, Vol.24 (1), p.73-77
Main Authors: Eastment, H. T., Krzanowski, W. J.
Format: Article
Language:English
Subjects:
Coordinate systems
Correlations
Covariance matrices
Cross-validation
Datasets
Dimensionality reduction
Eigenvalues
Eigenvectors
Matrices
Modeling
Principal component analysis
Principal components analysis
Reduction of dimensionality
Singular value decomposition
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Summary:A method is described for choosing the number of components to retain in a principal component analysis when the aim is dimensionality reduction. The correspondence between principal component analysis and the singular value decomposition of the data matrix is used. The method is based on successively predicting each element in the data matrix after deleting the corresponding row and column of the matrix, and makes use of recently published algorithms for updating a singular value decomposition. These are very fast, which renders the proposed technique a practicable one for routine data analysis.
ISSN:0040-1706
1537-2723
DOI:10.1080/00401706.1982.10487712