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Scaling variables and interpretation of eigenvalues in principal component analysis of geologic data

Journal of the International Association for Mathematical Geology

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DOI: 10.1007/BF01034742

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Abstract

The dominant feature distinguishing one method of principal components analysis from another is the manner in which the original data are transformed prior to the other computations. The only other distinguishing feature of any importance is whether the eigenvectors of the inner product-moment of the transformed data matrix are taken directly as the Q-mode scores or scaled by the square roots of their associated eigenvalues and called the R-mode loadings. If the eigenvectors are extracted from the product-moment correlation matrix, the variables, in effect, were transformed by column standardization (zero means and unit variances), and the sum of the p-largest eigenvalues divided by the sum of all the eigenvalues indicates the degree to which a model containing p components will account for the total variance in the original data. However, if the data were transformed in any manner other than column standardization, the eigenvalues cannot be used in this manner, but can only be used to determine the degree to which the model will account for the transformed data. Regardless of the type of principal components analysis that is performed-even whether it is R or Q-mode-the goodness-of-fit of the model to the original data is given better by the eigenvalues of the correlation matrix than by those of the matrix that was actually factored. ?? 1980 Plenum Publishing Corporation.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Scaling variables and interpretation of eigenvalues in principal component analysis of geologic data
Series title:
Journal of the International Association for Mathematical Geology
DOI:
10.1007/BF01034742
Volume
12
Issue:
6
Year Published:
1980
Language:
English
Publisher location:
Kluwer Academic Publishers-Plenum Publishers
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
Larger Work Title:
Journal of the International Association for Mathematical Geology
First page:
523
Last page:
538
Number of Pages:
16