discriminatory_crit {ICSClust}

Selection of ICS components based on discriminatory power

Description

Identifies invariant coordinates associated to the highest discriminatory power (by default "eta2").

Usage

discriminatory_crit(object, ...)

## S3 method for class 'ICS'
discriminatory_crit(
  object,
  clusters,
  method = "eta2",
  nb_select = NULL,
  select_only = FALSE,
  ...
)

## Default S3 method:
discriminatory_crit(
  object,
  clusters,
  method = "eta2",
  nb_select = NULL,
  select_only = FALSE,
  gen_kurtosis = NULL,
  ...
)

Arguments

object

dataframe or object of class "ICS".

...

additional arguments are currently ignored.

clusters

a vector of the same length as the number of observations, indicating the true clusters. It is used to compute the discriminatory power based on it.

method

the name of the discriminatory power. Only "eta2" is implemented.

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 clusters minus one.

select_only

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

gen_kurtosis

vector of generalized kurtosis values.

Details

The discriminatory power \eta^{2} = 1 - \Lambda, where \Lambda denotes Wilks' lambda, is evaluated for each combination of the first and/or last combinations of nb_select components. The combination achieving the highest discriminatory power is selected.

More specifically, we compute

\eta^{2} = 1 - \frac{\det(E)}{\det(T)},

where E is the within-group sum of squares and cross-products matrix and T is the total sum of squares and cross-products matrix.

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 "discriminatory".

• method: the name of the discriminatory power.

• nb_select: the number of components to select.

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

• power_combinations: the discriminatory values for each of the considered combinations of nb_select components.

• gen_kurtosis: the vector of generalized kurtosis values in case of ICS object.

Author(s)

Aurore Archimbaud and Anne Ruiz-Gazen

References

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

See Also

normal_crit(), med_crit(), var_crit().

Examples

X <- iris[,-5]
out <- ICS(X)
discriminatory_crit(out, clusters = iris[,5], select_only = FALSE)