Type: Package
Title: High Dimensional Discriminant Analysis with Compositional Data
Version: 1.0
Date: 2025-07-08
Maintainer: Michail Tsagris <mtsagris@uoc.gr>
Depends: R (≥ 4.0)
Imports: Compositional, HDclassif, Rfast, stats
Suggests: Rfast2
Description: High dimensional discriminant analysis with compositional data is performed. The compositional data are first transformed using the alpha-transformation of Tsagris M., Preston S. and Wood A.T.A. (2011) <doi:10.48550/arXiv.1106.1451>, and then the High Dimensional Discriminant Analysis (HDDA) algorithm of Bouveyron C. Girard S. and Schmid C. (2007) <doi:10.1080/03610920701271095> is applied.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
NeedsCompilation: no
Packaged: 2025-07-08 20:13:08 UTC; mtsag
Author: Michail Tsagris [aut, cre]
Repository: CRAN
Date/Publication: 2025-07-11 13:10:02 UTC

High Dimensional Discriminant Analysis with Compositional Data

Description

High dimensional discriminant analysis (HDDA) for compositional data using the alpha-transformation is performed.

Details

Package: CompositionalHDDA
Type: Package
Version: 1.0
Date: 2025-07-08
License: GPL-2

Maintainers

Michail Tsagris <mtsagris@uoc.gr>

Author(s)

Michail Tsagris mtsagris@uoc.gr.

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

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)

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.

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.

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.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

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)

Cross-Validation of the HDDA for compositional data using the alpha-transformation

Description

Cross-Validation of the HDDA for compositional data using the alpha-transformation.

Usage

cv.alfahdda(ina, x, a = seq(-1, 1, by = 0.1), d_select = "both", 
threshold = c(0.001, 0.005, 0.05, 1:9 * 0.1), folds = NULL, stratified = TRUE, 
nfolds = 10, seed = NULL)

Arguments

ina

A group indicator variable for the compositional data.

x

The compositional data. Zero values are allowed.

a

A vector of \alpha values.

d_select

Either "Cattell", "BIC" or "both".

threshold

A vector with numbers strictly bewtween 0 and 1. Each value corresponds to a threshold used in the Cattell's Scree-Test.

folds

If you have the list with the folds supply it here. You can also leave it NULL and it will create folds.

stratified

Do you want the folds to be created in a stratified way? The default value is TRUE.

nfolds

The number of folds in the cross validation.

seed

You can specify your own seed number here or leave it NULL.

Details

K-fold cross-validation for the high dimensional discriminant analysis with compositional data using the \alpha-transformation is performed.

Value

A list including:

kl

A matrix with the configurations of hyper-parameters tested and the estimated Kullback-Leibler divergence, for each configuration.

js

A matrix with the configurations of hyper-parameters tested and the estimated Jensen-Shannon divergence, for each configuration.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

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

alfa.hdda

Examples

x <- matrix( rgamma(100 * 200, runif(200, 4, 10), 1), ncol = 200, byrow = TRUE )
x <- x / rowSums(x)  ## Dirichlet simulated values
ina <- rbinom(100, 1, 0.5)
mod <- cv.alfahdda(ina, x, a = c(0.1, 0.5, 1), d_select = "both", 
threshold = seq(0.1, 0.5, by = 0.1), nfolds = 5)