Inferring Hierarchical Mixture Structures: A Bayesian Nonparametric Approach

We present a Bayesian Nonparametric model for Hierarchical Clustering (HC). Such a model has two main components. The first component is the random walk process from parent to child in the hierarchy and we apply nested Chinese Restaurant Process (nCRP). Then, the second part is the diffusion process from parent to child where we employ Hierarchical Dirichlet Process Mixture Model (HDPMM). This is different from the common choice which is Gaussian-to-Gaussian. We demonstrate the properties of the model and propose a Markov Chain Monte Carlo procedure with elegantly analytical updating steps for inferring the model variables. Experiments on the real-world datasets show that our method obtains reasonable hierarchies and remarkable empirical results according to some well known metrics.