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movMF: An R Package for Fitting Mixtures of von Mises-Fisher Distributions

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  • Hornik, Kurt
  • Grün, Bettina

Abstract

Finite mixtures of von Mises-Fisher distributions allow to apply model-based clustering methods to data which is of standardized length, i.e., all data points lie on the unit sphere. The R package movMF contains functionality to draw samples from finite mixtures of von Mises-Fisher distributions and to fit these models using the expectation-maximization algorithm for maximum likelihood estimation. Special features are the possibility to use sparse matrix representations for the input data, different variants of the expectation-maximization algorithm, different methods for determining the concentration parameters in the M-step and to impose constraints on the concentration parameters over the components. In this paper we describe the main fitting function of the package and illustrate its application. In addition we compare the clustering performance of finite mixtures of von Mises-Fisher distributions to spherical k-means. We also discuss the resolution of several numerical issues which occur for estimating the concentration parameters and for determining the normalizing constant of the von Mises-Fisher distribution.

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  • 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).
    • Handle: RePEc:jss:jstsof:v:058:i10
    DOI: http://hdl.handle.net/10.18637/jss.v058.i10
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    References listed on IDEAS

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    1. Feinerer, Ingo & Hornik, Kurt & Meyer, David, 2008. "Text Mining Infrastructure in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 25(i05).
    2. Hornik, Kurt, 2005. "A CLUE for CLUster Ensembles," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i12).
    3. Suvrit Sra, 2012. "A short note on parameter approximation for von Mises-Fisher distributions: and a fast implementation of I s (x)," Computational Statistics, Springer, vol. 27(1), pages 177-190, March.
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    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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    Cited by:

    1. Giuseppe Pandolfo & Antonio D’ambrosio, 2023. "Clustering directional data through depth functions," Computational Statistics, Springer, vol. 38(3), pages 1487-1506, September.
    2. 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.
    3. Vaidehi Dixit & Ryan Martin, 2022. "Estimating a Mixing Distribution on the Sphere Using Predictive Recursion," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 596-626, November.
    4. Mercedes Fernandez Sau & Daniela Rodriguez, 2018. "Minimum distance method for directional data and outlier detection," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(3), pages 587-603, September.
    5. Tin Lok James Ng, 2023. "Penalized maximum likelihood estimator for mixture of von Mises–Fisher distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(2), pages 181-203, February.
    6. Felix Mbuga & Cristina Tortora, 2021. "Spectral Clustering of Mixed-Type Data," Stats, MDPI, vol. 5(1), pages 1-11, December.
    7. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    8. Davy Paindaveine & Thomas Verdebout, 2017. "Detecting the Direction of a Signal on High-dimensional Spheres: Non-null and Le Cam Optimality Results," Working Papers ECARES ECARES 2017-40, ULB -- Universite Libre de Bruxelles.
    9. Xu, Hang & Alvo, Mayer & Yu, Philip L.H., 2018. "Angle-based models for ranking data," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 113-136.
    10. You, Kisung & Suh, Changhee, 2022. "Parameter estimation and model-based clustering with spherical normal distribution on the unit hypersphere," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    11. Soukissian, Takvor H. & Karathanasi, Flora E., 2017. "On the selection of bivariate parametric models for wind data," Applied Energy, Elsevier, vol. 188(C), pages 280-304.
    12. Xavier Bry & Lionel Cucala, 2022. "A von Mises–Fisher mixture model for clustering numerical and categorical variables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 429-455, June.

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