var_crit {ICSClust}

Selection of Invariant components using the var criterion

Description

Identifies the interesting invariant coordinates based on the rolling variance criterion as used in the ICSboot function of the ICtest package. It computes rolling variances on the generalized eigenvalues obtained through ICS::ICS().

Usage

var_crit(object, ...)

## S3 method for class 'ICS'
var_crit(object, nb_select = NULL, select_only = FALSE, ...)

## Default S3 method:
var_crit(object, nb_select = NULL, select_only = FALSE, ...)

Arguments

object

object of class "ICS".

...

additional arguments are currently ignored.

nb_select

the exact number of components to select. By default it is set to NULL, i.e the number of components to select is the number of variables minus one.

select_only

boolean. If TRUE only the vector names of the selected invariant components is returned. If FALSE additional details are returned.

Details

Assuming that the generalized eigenvalues of the uninformative components are all the same means that the variance of these generalized eigenvalues must be minimal. Therefore when nb_select components should be selected, the method identifies the p - nb_select neighboring generalized eigenvalues with minimal variance, where p is the total number of components. The number of interesting components should be at most p-2 as at least two uninteresting components are needed to compute a variance.

Value

If select_only is TRUE a vector of the names of the invariant components or variables to select. If FALSE an object of class "ICS_crit" is returned with the following objects:

• crit: the name of the criterion "var".

• nb_select: the number of components to select.

• gen_kurtosis: the vector of generalized kurtosis values.

• select: the names of the invariant components or variables to select.

• RollVarX: the rolling variances of order d-nb_select.

• Order: indexes of the ordered invariant components such that the ones associated to the smallest variances of the eigenvalues are at the end.

Author(s)

Andreas Alfons, Aurore Archimbaud and Klaus Nordhausen

References

Alfons, A., Archimbaud, A., Nordhausen, K., & Ruiz-Gazen, A. (2022). Tandem clustering with invariant coordinate selection. arXiv preprint arXiv:2212.06108..

Radojicic, U., & Nordhausen, K. (2019). Non-gaussian component analysis: Testing the dimension of the signal subspace. In Workshop on Analytical Methods in Statistics (pp. 101–123). Springer. doi:10.1007/978-3-030-48814-7_6.

See Also

normal_crit(), med_crit(), discriminatory_crit().

Examples

X <- iris[,-5]
out <- ICS(X)
var_crit(out, nb_select = 2, select_only = FALSE)