# mix.vmf: Mixtures of Von Mises-Fisher distributions In Directional: Directional Statistics

## Description

It performs model based clustering for circualr, spherical and hyperspherical data assuming von Mises-Fisher distributions.

## Usage

 `1` ```mix.vmf(x, g ,n.start = 20) ```

## 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.

## Details

The initial step of the algorithm is not based on a spherical k-means, but on s imple k-means. The results are comparable to the package movMF.

## Value

A list including:

 `param` A matrix with the mean direction, the concetrations parameter and mixing probability of each group. `loglik` The value of the maximised log-likelihood. `pred` The predicted group of each observation. `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

R implementation and documentation: Michail Tsagris <[email protected]> and Giorgos Athineou <[email protected]>

## 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

```rmixvmf, bic.mixvmf, mixvmf.contour ```
 ```1 2 3 4 5 6 7 8``` ```k <- runif(4, 4, 20) 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 mix.vmf(x, 3) mix.vmf(x, 4) mix.vmf(x, 5) ```