alg.CU: CU quantile-based clustering algorithm

In QuClu: Quantile-Based Clustering Algorithms

CU quantile-based clustering algorithm

Description

This function allows to run the CU (Common theta and Unscaled variables) version of the quantile-based clustering algorithm.

Usage

alg.CU(data, k = 2, eps = 1e-08, it.max = 100, B = 30)

Arguments

data	A numeric vector, matrix, or data frame of observations. Categorical variables are not allowed. If a matrix or data frame, rows correspond to observations and columns correspond to variables.
k	The number of clusters. The default is k=2.
eps	The relative convergence tolerances for objective function. The default is set to 1e-8.
it.max	A number that gives integer limits on the number of the CU algorithm iterations. By default, it is set to 100.
B	The number of times the initialization step is repeated; the default is 30.

Details

Algorithm CU: Common theta and Unscaled variables. A common value of theta for all the variables is assumed. This strategy directly generalizes the conventional k-means to other moments of the distribution to better accommodate skewness in the data.

Value

A list containing the following elements:

method	The chosen parameterization, CU, Common theta and Unscaled variables
k	The number of clusters.
cl	A vector whose [i]th entry is classification of observation i in the test data.
qq	A matrix whose [h,j]th entry is the theta-quantile of variable j in cluster h.
theta	A vector whose [j]th entry is the percentile theta for variable j.
Vseq	The values of the objective function V at each step of the algorithm.
V	The final value of the objective function V.
lambda	A vector containing the scaling factor for each variable.

References

Hennig, C., Viroli, C., Anderlucci, L. (2019) "Quantile-based clustering" Electronic Journal of Statistics, 13 (2) 4849-4883 <doi:10.1214/19-EJS1640>

Examples

out <- alg.CU(iris[,-5],k=3)
out$theta
out$qq

table(out$cl)

QuClu documentation built on May 28, 2022, 1:22 a.m.