Compositional (version 5.5)

Cross validation for the alpha-k-NN regression with compositional response data: Cross validation for the \(\alpha\)-k-NN regression with compositional response data

Description

Cross validation for the \(\alpha\)-k-NN regression with compositional response data.

Usage

aknnreg.tune(y, x, a = seq(0.1, 1, by = 0.1), k = 2:10, apostasi = "euclidean",
nfolds = 10, folds = NULL, seed = NULL, rann = FALSE)

Arguments

y

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

x

A matrix with the available predictor variables.

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.

k

The number of nearest neighbours to consider. It can be a single number or a vector.

apostasi

The type of distance to use, either "euclidean" or "manhattan".

nfolds

The number of folds. Set to 10 by default.

folds

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

seed

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

rann

If you have large scale datasets and want a faster k-NN search, you can use kd-trees implemented in the R package "RANN". In this case you must set this argument equal to TRUE. Note however, that in this case, the only available distance is by default "euclidean".

Value

A list including:

kl

The Kullback-Leibler divergence for all combinations of \(\alpha\) and \(k\).

js

The Jensen-Shannon divergence for all combinations of \(\alpha\) and \(k\).

klmin

The minimum Kullback-Leibler divergence.

jsmin

The minimum Jensen-Shannon divergence.

kl.alpha

The optimal \(\alpha\) that leads to the minimum Kullback-Leibler divergence.

kl.k

The optimal \(k\) that leads to the minimum Kullback-Leibler divergence.

js.alpha

The optimal \(\alpha\) that leads to the minimum Jensen-Shannon divergence.

js.k

The optimal \(k\) that leads to the minimum Jensen-Shannon divergence.

runtime

The runtime of the cross-validation procedure.

Details

A k-fold cross validation for the \(\alpha\)-k-NN regression for compositional response data is performed.

References

Michail Tsagris, Abdulaziz Alenazi and Connie Stewart (2021). Non-parametric regression models for compositional data. https://arxiv.org/pdf/2002.05137.pdf

See Also

aknn.reg, akernreg.tune, akern.reg, alfa.rda, alfa.fda, rda.tune

Examples

# NOT RUN {
y <- as.matrix( iris[, 1:3] )
y <- y / rowSums(y)
x <- iris[, 4]
mod <- aknnreg.tune(y, x, a = c(0.4, 0.6), k = 2:4, nfolds = 5)
# }