alfa.pca: Principal component analysis using the alpha-transformation

In Compositional: Compositional Data Analysis

Principal component analysis using the \alpha-transformation

Description

Principal component analysis using the \alpha-transformation.

Usage

alfa.pca(x, a, center = TRUE, scale = TRUE, k = NULL, vectors = FALSE)

Arguments

x	A matrix with the compositional data. Zero values are allowed. In that case "a" should be positive.
a	The value of \alpha to use in the \alpha-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.

Details

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).

Value

A list including:

values	The eigenvalues.
vectors	The eigenvectors.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

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

See Also

logpca, alfa.pcr, kl.alfapcr

Examples

x <- as.matrix(iris[, 1:4])
x <- x/ rowSums(x)
a <- alfa.pca(x, 0.5)

Compositional documentation built on Oct. 9, 2024, 5:10 p.m.