Tuning of the k-NN algorithm for compositional data {Compositional} R Documentation

## Tuning of the k-NN algorithm for compositional data

### Description

Tuning of the k-NN algorithm for compositional data with and without using the power or the α-transformation. In addition, estimation of the rate of correct classification via M-fold cross-validation.

### Usage

```compknn.tune(x, ina, nfolds = 10, k = 2:5, type= "S", mesos = TRUE,
a = seq(-1, 1, by = 0.1), apostasi = "ESOV", folds = NULL,
stratified = FALSE, seed = FALSE, graph = FALSE)

alfaknn.tune(x, ina, nfolds = 10, k = 2:5, type = "S", mesos = TRUE,
a = seq(-1, 1, by = 0.1), apostasi = "euclidean", rann = FALSE, folds = NULL,
stratified = FALSE, seed = FALSE, graph = FALSE)

aitknn.tune(x, ina, nfolds = 10, k = 2:5, type = "S", mesos = TRUE,
a = seq(-1, 1, by = 0.1), apostasi = "euclidean", rann = FALSE, folds = NULL,
stratified = FALSE, seed = FALSE, graph = FALSE)
```

### Arguments

 `x` A matrix with the available compositional data. Zeros are allowed, but you must be careful to choose strictly positive values of α or not to set apostasi= "Ait". `ina` A group indicator variable for the available data. `nfolds` The number of folds to be used. This is taken into consideration only if the folds argument is not supplied. `k` A vector with the nearest neighbours to consider. `type` This can be either "S" for the standard k-NN or "NS" for the non standard (see details). `mesos` This is used in the non standard algorithm. If TRUE, the arithmetic mean of the distances is calculated, otherwise the harmonic mean is used (see details). `a` A grid of values of α to be used only if the distance chosen allows for it. `apostasi` The type of distance to use. For the compk.knn this can be one of the following: "ESOV", "taxicab", "Ait", "Hellinger", "angular" or "CS". See the references for them. For the alfa.knn this can be either "euclidean" or "manhattan". `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". `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? TRUE or FALSE. `seed` If seed is TRUE the results will always be the same. `graph` If set to TRUE a graph with the results will appear.

### Details

The k-NN algorithm is applied for the compositional data. There are many metrics and possibilities to choose from. The standard algorithm finds the k nearest observations to a new observation and allocates it to the class which appears most times in the neighbours. The non standard algorithm is slower but perhaps more accurate. For every group is finds the k nearest neighbours to the new observation. It then computes the arithmetic or the harmonic mean of the distances. The new point is allocated to the class with the minimum distance.

### Value

A list including:

 `ela` A matrix or a vector (depending on the distance chosen) with the averaged over all folds rates of correct classification for all hyper-parameters (α and k). `performance` The estimated rate of correct classification. `best_a` The best value of α. This is returned for "ESOV" and "taxicab" only. `best_k` The best number of nearest neighbours. `runtime` The run time of the cross-validation procedure.

### Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Giorgos Athineou <gioathineou@gmail.com>.

### References

Tsagris, Michail (2014). The k-NN algorithm for compositional data: a revised approach with and without zero values present. Journal of Data Science, 12(3): 519-534. https://arxiv.org/pdf/1506.05216.pdf

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

Tsagris Michail, Simon Preston and Andrew T.A. Wood (2016). Improved classification for compositional data using the α-transformation. Journal of classification 33(2): 243-261. https://arxiv.org/pdf/1506.04976v2.pdf

Connie Stewart (2017). An approach to measure distance between compositional diet estimates containing essential zeros. Journal of Applied Statistics 44(7): 1137-1152.

Clarotto L., Allard D. and Menafoglio A. (2021). A new class of α-transformations for the spatial analysis of Compositional Data. https://arxiv.org/abs/2110.07967

Endres, D. M. and Schindelin, J. E. (2003). A new metric for probability distributions. Information Theory, IEEE Transactions on 49, 1858-1860.

Osterreicher, F. and Vajda, I. (2003). A new class of metric divergences on probability spaces and its applicability in statistics. Annals of the Institute of Statistical Mathematics 55, 639-653.

```comp.knn, alfarda.tune, cv.dda, cv.compnb ```

### Examples

```x <- as.matrix(iris[, 1:4])
x <- x/ rowSums(x)
ina <- iris[, 5]
mod1 <- compknn.tune(x, ina, a = seq(1, 1, by = 0.1) )
mod2 <- alfaknn.tune(x, ina, a = seq(-1, 1, by = 0.1) )
```

[Package Compositional version 5.2 Index]