Principal coordinate analysis using the alpha-distance {Compositional}

Principal coordinate analysis using the \alpha-distance

Description

Principal coordinate analysis using the \alpha-distance.

Usage

alfa.mds(x, a, k = 2, eig = TRUE)

Arguments

x

A matrix with the compositional data. Zero values are allowed.

a

The value of a. In case of zero values in the data it has to be greater than 1.

k

The maximum dimension of the space which the data are to be represented in. This can be a number between 1 and D-1, where D denotes the number of dimensions.

eig

Should eigenvalues be returned? The default value is TRUE.

Details

The function computes the \alpha-distance matrix and then plugs it into the classical multidimensional scaling function in the "cmdscale" function.

Value

A list with the results of "cmdscale" function.

Author(s)

Michail Tsagris.

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

References

Aitchison J. (1986). The statistical analysis of compositional data. Chapman & Hall.

Cox, T. F. and Cox, M. A. A. (2001). Multidimensional Scaling. Second edition. Chapman and Hall.

Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979). Chapter 14 of Multivariate Analysis, London: Academic Press.

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. https://arxiv.org/pdf/1106.1451.pdf

See Also

esov.mds, alfa.pca,

Examples

  x <- as.matrix(iris[, 1:4])
  x <- x/ rowSums(x)
  a <- esov.mds(x)