Cross validation for the alpha-k-NN regression for compositional response data {Compositional} R Documentation

## Cross validation for the α-k-NN regression for compositional response data

### Description

Cross validation for the α-k-NN regression for 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 = FALSE, 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 α=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` If seed is TRUE the results will always be the same. `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".

### Details

A k-fold cross validation for the α-k-NN regression for compositional response data is performed.

### Value

A list including:

 `kl` The Kullback-Leibler divergence for all combinations of α and k. `js` The Jensen-Shannon divergence for all combinations of α and k. `klmin` The minimum Kullback-Leibler divergence. `jsmin` The minimum Jensen-Shannon divergence. `kl.alpha` The optimal α 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 α 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.

### Author(s)

Michail Tsagris.

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

### References

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

`aknn.reg, akernreg.tune, akern.reg, alfa.rda, alfa.fda, rda.tune `
```y <- as.matrix( iris[, 1:3] )