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.
Highlights
Clustering data in the unit sphere is an important task in modern data analysis, for example, in clustering text documents when analysing textual data.One approach to address such issue is the spherical k-means clustering
Other works that have appeared in the literature for clustering directional data are based on model-based clustering methods
Peel et al (2001) [3] used the Kent distribution [4] to form groups of fracture data through a model-based clustering and Dortet-Bernadet and Wicker (2008) [5] supposed a model-based clustering of data that lies on a unit sphere and applied this clustering method to gene expression profiles
Summary
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
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