UCM {PUGMM}

Ultrametric Correlation Matrix

Description

Fit an ultrametric correlation matrix on a nonnegative correlation one.

Usage

UCM(R, m, rndstart, maxiter = 100, eps = 1e-06)

Arguments

R

(p \times p) nonnegative correlation matrix.

m

Integer specifying the number of variable groups.

rndstart

Integer value specifying the number of random starts.

maxiter

Integer value specifying the maximum number of iterations of the EM algorithm (default: maxiter = 100).

eps

Numeric value specifying the tolerance for the convergence criterion used in the coordinate descent algorithm (default: eps = 1e-6).

Value

A list with the following elements:

call Matched call.

V Optimal binary and row-stochastic (p \times m) variable-group membership matrix.

Rt Optimal (p \times p) ultrametric correlation matrix.

Rw Optimal (m \times m) within-concept consistency (diagonal) matrix.

Rb Optimal (m \times m) between-concept correlation matrix.

of Objective function corresponding to the optimal solution.

loop Random start corresponding to the optimal solution.

iter Number of iterations needed to obtain the optimal solution.

References

Cavicchia, C., Vichi, M., Zaccaria, G. (2020) The ultrametric correlation matrix for modelling hierarchical latent concepts. Advances in Data Analysis and Classification, 14(4), 837-853.

Examples

data(penguins)
R <- cor(penguins[, 2:5])
UCM(R, 4, 1)