Sparse mixture of von Mises-Fisher distribution

International audienceMixtures of von Mises-Fisher distributions can be used to cluster data on the unit hypersphere. This is particularly adapted for high-dimensional directional data such as texts. We propose in this article to estimate a von Mises mixture using a l1 penalized likelihood. This leads to sparse prototypes that improve both clustering quality and interpretability. We introduce an expectation-maximisation (EM) algorithm for this estimation and show the advantages of the approach on real data benchmark. We propose to explore the trade-off between the sparsity term and the likelihood one with a simple path following algorithm