document: Generative model-based clustering of directional data High dimensional directional data is becoming increasingly important in contemporary applications such as analysis of text and gene-expression data . A natural model for multi-variate directional data is provided by the von Mises-Fisher ( vMF ) distribution on the unit hypersphere that is analogous to the multi-variate Gaussian distribution in Rd. . In this paper , we propose modeling complex directional data as a mixture of vMF distributions . We derive and analyze two variants of the Expectation Maximization ( EM ) framework for estimating the parameters of this mixture . We also propose two clustering algorithms corresponding to these variants . An interesting aspect of our methodology is that the spherical kmeans algorithm ( kmeans with cosine similarity ) can be shown to be a special case of both our algorithms . Thus , modeling text data by vMF distributions lends theoretical validity to the use of cosine similarity which has been widely used by the information retrieval community . As part of experimental validation , we present results on modeling high-dimensional text and gene-expression data as a mixture of vMF distributions . The results indicate that our approach yields superior clusterings especially for difficult clustering tasks in high-dimensional spaces .
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