Principal component analysis using the \(\alpha\)-transformation.
alfa.pca(x, a, center = TRUE, scale = TRUE, k = NULL, vectors = FALSE)A matrix with the compositional data. Zero values are allowed. In that case "a" should be positive.
The value of \(\alpha\) to use in the \(\alpha\)-transformation.
Do you want your data centered? TRUE or FALSE.
Do you want each of your variables scaled, i.e. to have unit variance? TRUE or FALSE.
If you want a specific number of eigenvalues and eigenvectors set it here, otherwise all eigenvalues (and eigenvectors if requested) will be returned.
Do you want the eigenvectors be returned? By dafault this is FALSE.
A list including:
The eigenvalues.
The eigenvectors.
The \(\alpha\)-transformation is applied to the compositional data and then PCA is performed. Note however, that the right multiplication by the Helmert sub-matrix is not applied in order to be in accordance with Aitchison (1983). When \(\alpha=0\), this results to the PCA proposed by Aitchison (1983).
Aitchison J. (1986). The statistical analysis of compositional data. Chapman & Hall.
Aitchison, J. (1983). Principal component analysis of compositional data. Biometrika, 70(1), 57-65.
Tsagris M.T., Preston S. and Wood A.T.A. (2011). A data-based power transformation for compositional data. In Proceedings of the 4th Compositional Data Analysis Workshop, Girona, Spain. http://arxiv.org/pdf/1106.1451.pdf
# NOT RUN {
x <- as.matrix(iris[, 1:4])
x <- x/ rowSums(x)
a <- alfa.pca(x, 0.5)
# }
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