mixvmf.mle: Mixtures of rotationally symmetric distributions

In Directional: A Collection of Functions for Directional Data Analysis

Mixtures of rotationally symmetric distributions

Description

It performs model based clustering for circualr, spherical and hyper-spherical data assuming rotationally symetric distributions.

Usage

mixvmf.mle(x, g, n.start = 5, tol = 1e-6, maxiters = 100)
mixspcauchy.mle(x, g, n.start = 5, tol = 1e-6, maxiters = 100)
mixpkbd.mle(x, g, n.start = 5, tol = 1e-6, maxiters = 100)

Arguments

x	A matrix with the data expressed as unit vectors.
g	The number of groups to fit. It must be greater than or equal to 2.
n.start	The number of random starts to try. See also R's built-in function kmeans for more information about this.
tol	The tolerance value to terminate the EM algorithm.
maxiters	The maximum number of iterations to perform.

Details

The initial step of the algorithm is not based on a spherical k-means, but on simple k-means. The results are comparable to the package movMF for the mixtures of von Mises-Fisher distributions. The other cases are mixtures of spherical Cauchy distributions or mixtures of Poisson kernel-based distributions.

Value

A list including:

param	A matrix with the mean direction, the concentration parameters and mixing probability of each group.
loglik	The value of the maximised log-likelihood.
pred	The predicted group of each observation.
w	The estimated probabilities of each observation to belong to each cluster.
iter	The number of iteration required by the EM algorithm.
runtime	The run time of the algorithm. A numeric vector. The first element is the user time, the second element is the system time and the third element is the elapsed time.

Author(s)

Michail Tsagris and Panagiotis Papastamoulis.

R implementation and documentation: Michail Tsagris [e-mail] and Panagiotis Papastamoulis [e-mail].

References

Kurt Hornik and Bettina Grun (2014). movMF: An R Package for Fitting Mixtures of von Mises-Fisher Distributions http://cran.r-project.org/web/packages/movMF/vignettes/movMF.pdf

Tsagris M. and Papastamoulis P. (2024). Directional data analysis using the spherical Cauchy and the Poisson kernel-based distribution. https://arxiv.org/pdf/2409.03292.

See Also

rmixvmf, bic.mixvmf, mixvmf.contour

Examples

k <- runif(4, 4, 6)
prob <- c(0.2, 0.4, 0.3, 0.1)
mu <- matrix(rnorm(16), ncol = 4)
mu <- mu / sqrt( rowSums(mu^2) )
x <- rmixvmf(200, prob, mu, k)$x
mixvmf.mle(x, 3)
mixvmf.mle(x, 4)
mixvmf.mle(x, 5)

Directional documentation built on Oct. 30, 2024, 9:15 a.m.