K-means++ for mixtures of von Mises-Fisher Distributions

Abstract

Von Mises-Fisher (vMF) Distribution is one of the most commonly used distributions for fitting directional data. Mixtures of vMF (MovMF) distributions have been used successfully in many applications. One of the important problems in mixture models is the problem of local minima of the objective function. Therefore, approaches to avoid local minima problem is essential in improving the performance. Recently, an algorithm called k-means++ was introduced in the literature and used successfully for finding initial parameters for mixtures of Gaussian (MoG) distributions. In this paper, we adopt this algorithm for finding good initializations for MovMF distributions. We show that MovMF distribution will lead to the same cost function as MoGs and therefore similar guarantee as the case of MoG distributions will also hold here. We also demonstrate the performance of the method on some real datasets.