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

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  • Adelaide Figueiredo

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

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.

Suggested Citation

  • Adelaide Figueiredo, 2017. "Clustering Directions Based on the Estimation of a Mixture of Von Mises-Fisher Distributions," The Open Statistics and Probability Journal, Bentham Open, vol. 8(1), pages 39-52, December.
    • Handle: RePEc:ben:tostpj:v:8:y:2017:i:1:p:39-52
    DOI: 10.2174/1876527001708010039
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    References listed on IDEAS

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    1. Hornik, Kurt & Grün, Bettina, 2014. "movMF: An R Package for Fitting Mixtures of von Mises-Fisher Distributions," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 58(i10).
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    3. Celeux, Gilles & Govaert, Gerard, 1992. "A classification EM algorithm for clustering and two stochastic versions," Computational Statistics & Data Analysis, Elsevier, vol. 14(3), pages 315-332, October.
    4. Hornik, Kurt & Feinerer, Ingo & Kober, Martin & Buchta, Christian, 2012. "Spherical k-Means Clustering," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 50(i10).
    5. Peel D. & Whiten W. J & McLachlan G. J, 2001. "Fitting Mixtures of Kent Distributions to Aid in Joint Set Identification," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 56-63, March.
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