Directional (version 7.0)

Mixtures of rotationally symmetric distributions: 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)

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.

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.

Author

Michail Tsagris and Panagiotis Papastamoulis.

R implementation and documentation: Michail Tsagris and Panagiotis Papastamoulis .

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.

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., Papastamoulis P. and Kato S. (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)