CompositionalHDDA (version 1.0)

alfa.hdda: HDDA for compositional data using the alpha-transformation

Description

HDDA for compositional data using the alpha-transformation.

Usage

alfa.hdda(xnew, ina, x, a = seq(-1, 1, by = 0.1), d_select = "Cattell", threshold = 0.2)

Value

A list with sub-lists, one for each value of \(\alpha\), where each sub-list includes:

mod

A list containing the output as returned by the function hdda from the package HDclassif.

class

The predicted class of each observation.

posterior

The posterior probabilities of each new observation.

Arguments

xnew

A matrix with the new compositional data whose class is to be predicted.

ina

A group indicator variable for the compositional data.

x

The compositional data. Zero values are allowed.

a

Either a single value or a vector of \(\alpha\) values.

d_select

Either "Cattell", "BIC" or "both". "Cattell": The Cattell's scree-test is used to gather the intrinsic dimension of each class. If the model is of common dimension (models 7 to 14), the scree-test is done on the covariance matrix of the whole dataset.

"BIC": The intrinsic dimensions are selected with the BIC criterion. See Bouveyron et al. (2010) for a discussion of this topic. For common dimension models, the procedure is done on the covariance matrix of the whole dataset.

threshold

A float stricly within 0 and 1. It is the threshold used in the Cattell's Scree-Test.

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris .

Details

The compositional data are first using the \(\alpha\)-transformation and then the HDDA algorithm is called. The function then will compute all the models, give their BIC and keep the model with the highest BIC value.

References

Bouveyron C. Girard S. and Schmid C. (2007). High Dimensional Discriminant Analysis. Communications in Statistics: Theory and Methods, 36(14): 2607--2623.

Bouveyron C. Celeux G. and Girard S. (2010). Intrinsic dimension estimation by maximum likelihood in probabilistic PCA. Technical Report 440372, Universite Paris 1 Pantheon-Sorbonne.

Berge L. Bouveyron C. and Girard S. (2012). HDclassif: An R Package for Model-Based Clustering and Discriminant Analysis of High-Dimensional Data. Journal of Statistical Software, 46(6).

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

cv.alfahdda

Examples

x <- matrix( rgamma(60 * 100, runif(100, 4, 10), 1), ncol = 100, byrow = TRUE )
x <- x / rowSums(x)  ## Dirichlet simulated values
xnew <- matrix( rgamma(20 * 100, runif(100, 4, 10), 1), ncol = 100, byrow = TRUE )
xnew <- xnew / rowSums(xnew)  ## Dirichlet simulated values
ina <- rbinom(60, 1, 0.5)
alfa.hdda(xnew, ina, x, a = 0.5)