Clustering Directions Based on the Estimation of a Mixture of Von Mises-Fisher Distributions

Adelaide Figueiredo ()
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Adelaide Figueiredo: Faculty of Economics of University of Porto and LIAAD-INESC TEC, Porto, Portugal

The Open Statistics and Probability Journal, 2017, vol. 8, issue 1, 39-52

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.

Keywords: Directional data; Dynamic Clusters algorithm; EM algorithm; Hypersphere; Monte Carlo method; Simulation; Von Mises-Fisher distribution. (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:ben:tostpj:v:8:y:2017:i:1:p:39-52

DOI: 10.2174/1876527001708010039

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