The Open Mathematics, Statistics and Probability Journal
2017, 08 : 39-52Published online 2017 December 29. DOI: 10.2174/1876527001708010039
Publisher ID: TOSPJ-8-39
RESEARCH ARTICLE
Clustering Directions Based on the Estimation of a Mixture of Von Mises-Fisher Distributions
* Address correspondence to this author at the University of Porto, Faculty of Economics, Porto and LIAAD-INESC TEC, Portugal, Tel: (+351)220426449; E-mail: Adelaide@fep.up.pt
ABSTRACT
Background:
In the statistical analysis of directional data, the von Mises-Fisher distribution plays an important role to model unit vectors. The estimation of the parameters of a mixture of von Mises-Fisher distributions can be done through the Estimation-Maximization algorithm.
Objective:
In this paper we propose a dynamic clusters type algorithm based on the estimation of the parameters of a mixture of von Mises-Fisher distributions for clustering directions, and we compare this algorithm with the Estimation-Maximization algorithm. We also define the between-groups and within-groups variability measures to compare the solutions obtained with the algorithms through these measures.
Results:
The comparison of the clusters obtained with both algorithms is provided for a simulation study based on samples generated from a mixture of two Fisher distributions and for an illustrative example with spherical data.