Hierarchical von Mises-Fisher Mixture Model
Résumé
In this paper, we propose a complete method for clustering data, which are in the form of unit vectors. The solution consists of a distribution based clustering algorithm with the assumption of a generative model. In the model, the data is generated from a finite statistical mixture model based on the von Mises-Fisher (vMF) distribution. Initially, Bregman soft clustering algorithm is applied to obtain the parameters of the vMF mixture model (vMF-MM) for certain maximum number of components. Then, a hierarchy of mixture models is generated from the parameters. The hierarchy is generated by appropriately using Bregman divergence to compute dissimilarity among distributions as well as fuse/merge the centroids of the clusters. After constructing the hierarchy, Kullback Leibler divergence (KLD) is used to compute the distance between statistical mixture models with different number of components. Finally, a threshold (KLD value) is used to select number of components of the mixture model. The proposed method is called Hierarchical 3-D von Mises-Fisher mixture model. We validated the method by applying it on simulated data. Additionally, we applied the proposed method to cluster image normal, which are computed from the depth image. As an outcome of the clustering, we obtained a bottom-up segmentation of the depth image. Obtained results confirmed our assumption that the proposed method can be a potential tool to analyze depth images.