Compositional (version 1.5)

Cross validation for the regularised discriminant analysis with compositional data using the alpha-transformation: Cross validation for the regularised discriminant analysis with compositional data using the $\alpha$-transformation

Description

Cross validation for the regularised discriminant analysis with compositional data using the $\alpha$-transformation. Bias correction is applied using the TT estimate of bias (Tibshirani and Tibshirani, 2009). There is an option for the GCV criterion which is automatic. The predictor variables are compositional data and the $\alpha$-transformation is applied first.

Usage

alfarda.tune(x, ina, a = seq(-1, 1, by = 0.1), M = 10, gam = seq(0, 1, by = 0.1),
del = seq(0, 1, by = 0.1), ncores = 1, mat = NULL)

Arguments

x

A matrix with the available compositional data. Zeros are allowed.

ina

A group indicator variable for the avaiable data.

a

A vector with a grid of values of the power transformation, it has to be between -1 and 1. If zero values are present it has to be greater than 0. If $\alpha=0$ the isometric log-ratio transformation is applied.

M

The number of folds. Set to 10 by default.

gam

A vector of values between 0 and 1. It is the weight of the pooled covariance and the diagonal matrix.

del

A vector of values between 0 and 1. It is the weight of the LDA and QDA.

ncores

The number of cores to use. If it is more than 1 parallel computing is performed. It is advisable to use it if you have many observations and or many variables, otherwise it will slow down th process.

mat

You can specify your own folds by giving a mat, where each column is a fold. Each column contains indices of the observations. You can also leave it NULL and it will create folds.

Value

A list including:

res

The bias corrected estimated optimal rate, the estimated bias, the estimated standard error of the rate and the best values of $\alpha$, $gamma$ and $delta$.

percent

For the best value of $\alpha$ the averaged over all folds best prates of correct classification. It is a matrix, where rows correspond to the $\gamma$ values and columns correspond to $\delta$ values.

se

The estimated standard errors of the "percent" matrix.

runtime

The runtime of the cross-validation procedure.

Details

A k-fold cross validation is performed and the estimated performance is bias corrected as suggested by Tibshirani and Tibshirani (2009).

References

Friedman Jerome, Trevor Hastie and Robert Tibshirani (2009). The elements of statistical learning, 2nd edition. Springer, Berlin

Tsagris Michail, Simon Preston and Andrew TA Wood (2016). Improved classification for compositional data using the $\alpha$-transformation. Journal of classification (to appear). http://arxiv.org/pdf/1106.1451.pdf

Tibshirani R.J., and Tibshirani R. (2009). A bias correction for the minimum error rate in cross-validation. The Annals of Applied Statistics 3(2): 822-829.

See Also

alfa.rda, rda.tune

Examples

library(MASS)
x <- fgl[, 2:9]
ina <- fgl[, 10]
moda <- alfarda.tune(x, ina, a = seq(0.5, 1, by = 0.1), M = 10,
gam = seq(0, 0.7, by = 0.1), del = seq(0, 0.7, by = 0.1),
ncores = 1, mat = NULL)