Axial Data Modeling with Collapsed Nonparametric Watson Mixture Models and Its Application to Depth Image Analysis

Recently, axial data (i.e. the observations are axes of direction) have been involved with various fields ranging from blind speech separation to gene expression data clustering. In this paper, axial data modeling is performed by proposing a nonparametric infinite Watson mixture model which is constructed in a collapsed space (denoted by Co-InWMM) where the mixing coefficients are integrated out. Then, an effective collapsed variational Bayes (CVB) inference method is theoretically developed to learn the Co-InWMM with closed-from solutions. The proposed Co-InWMM with CVB inference for modeling axial data is validated through both synthetical data sets and a challenging application regarding depth image analysis.