Mixture of von Mises-Fisher distribution with sparse prototypes

TL;DR

This paper introduces a sparse, l1-penalized mixture of von Mises-Fisher distributions with an EM algorithm, enhancing clustering interpretability for high-dimensional directional data like texts and financial reports.

Contribution

It proposes a novel sparse estimation method for von Mises-Fisher mixtures using l1 penalty and develops an EM algorithm with a path following approach.

Findings

Improved clustering interpretability with sparse prototypes

Demonstrated advantages on simulated and real benchmark data

Effective exploratory analysis on financial reports

Abstract

Mixtures 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 l 1 penalized likelihood. This leads to sparse prototypes that improve clustering interpretability. We introduce an expectation-maximisation (EM) algorithm for this estimation and explore the trade-off between the sparsity term and the likelihood one with a path following algorithm. The model's behaviour is studied on simulated data and, we show the advantages of the approach on real data benchmark. We also introduce a new data set on financial reports and exhibit the benefits of our method for exploratory analysis.