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

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 \alpha-transformation. In addition, estimation of the rate of correct classification via K-fold cross-validation.

Usage

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

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

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

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 \alpha 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 "Rnanoflann". 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

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

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 algorithm finds the k nearest observations to a new observation and allocates it to the class which appears most times in the neighbours.

Value

A list including:

per

A matrix or a vector (depending on the distance chosen) with the averaged over all folds rates of correct classification for all hyper-parameters (\alpha and k).

performance

The estimated rate of correct classification.

best_a

The best value of \alpha. 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 [e-mail] and Giorgos Athineou <[e-mail]>.

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 M., Preston S. and Wood A.T.A. (2016). Improved classification for compositional data using the \alpha-transformation. Journal of Classification, 33(2): 243–261. http://arxiv.org/pdf/1106.1451.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. (2022). A new class of \alpha-transformations for the spatial analysis of Compositional Data. Spatial Statistics, 47.

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.

See Also

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) )