This paper aims at proposing an unsupervised hierarchical nonparametric Bayesian framework for modeling axial data (i.e., observations are axes of direction) that can be partitioned into multiple groups, where each observation within a group is sampled from a mixture of Watson distributions with an infinite number of components that are allowed to be shared across different groups. First, we propose a hierarchical nonparametric Bayesian model for modeling grouped axial data based on the hierarchical Pitman-Yor process mixture model of Watson distributions. Then, we demonstrate that by setting the discount parameters of the proposed model to 0, another hierarchical nonparametric Bayesian model based on hierarchical Dirichlet process can be derived for modeling axial data. To learn the proposed models, we systematically develop a closed-form optimization algorithm based on the collapsed variational Bayes (CVB) inference. Furthermore, to ensure the convergence of the proposed learning algorithm, an annealing mechanism is introduced to the framework of CVB inference, leading to an averaged collapsed variational Bayes inference strategy. The merits of the proposed models for modeling grouped axial data are demonstrated through experiments on both synthetic data and real-world applications involving gene expression data clustering and depth image analysis.

中文翻译：

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通过采用 Watson 分布的分层贝叶斯非参数模型进行无监督分组轴向数据建模


本文旨在提出一种无监督分层非参数贝叶斯框架，用于对轴向数据（即观测值是方向轴）进行建模，该框架可以分为多个组，其中组内的每个观测值都是从具有无限数量的 Watson 分布的混合中采样的允许在不同组之间共享的组件。首先，我们提出了一种分层非参数贝叶斯模型，用于基于 Watson 分布的分层 Pitman-Yor 过程混合模型对分组轴向数据进行建模。然后，我们证明，通过将所提出模型的折扣参数设置为 0，可以导出另一个基于分层狄利克雷过程的分层非参数贝叶斯模型，用于对轴向数据进行建模。为了学习所提出的模型，我们系统地开发了一种基于折叠变分贝叶斯（CVB）推理的封闭式优化算法。此外，为了确保所提出的学习算法的收敛性，在CVB推理框架中引入了退火机制，从而形成了平均折叠变分贝叶斯推理策略。通过对合成数据和涉及基因表达数据聚类和深度图像分析的实际应用的实验证明了所提出的用于对分组轴向数据进行建模的模型的优点。