Principal component analysis using the α-transformation
Principal component analysis using the α-transformation.
alfa.pca(x, a, center = TRUE, scale = TRUE, k = NULL, vectors = FALSE)
x |
A matrix with the compositional data. Zero values are allowed. In that case "a" should be positive. |
a |
The value of α to use in the α-transformation. |
center |
Do you want your data centered? TRUE or FALSE. |
scale |
Do you want each of your variables scaled, i.e. to have unit variance? TRUE or FALSE. |
k |
If you want a specific number of eigenvalues and eigenvectors set it here, otherwise all eigenvalues (and eigenvectors if requested) will be returned. |
vectors |
Do you want the eigenvectors be returned? By dafault this is FALSE. |
The α-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 α=0, this results to the PCA proposed by Aitchison (1983).
A list including:
values |
The eigenvalues. |
vectors |
The eigenvectors. |
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
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
x <- as.matrix(iris[, 1:4]) x <- x/ rowSums(x) a <- alfa.pca(x, 0.5)
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