Bayesian hierarchical mixture clustering (BHMC) improves on the traditional
Bayesian hierarchical clustering by, with regard to the parent-to-child
diffusion in the generative process, replacing the conventional
Gaussian-to-Gaussian (G2G) kernels with a Hierarchical Dirichlet Process
Mixture Model (HDPMM). However, the drawback of the BHMC lies in the
possibility of obtaining trees with comparatively high nodal variance in the
higher levels (i.e., those closer to the root node). This can be interpreted as
that the separation between the nodes, particularly those in the higher levels,
might be weak. We attempt to overcome this drawback through a recent
inferential framework named posterior regularization, which facilitates a
simple manner to impose extra constraints on a Bayesian model to address its
weakness. To enhance the separation of clusters, we apply posterior
regularization to impose max-margin constraints on the nodes at every level of
the hierarchy. In this paper, we illustrate the modeling detail of applying the
PR on BHMC and show that this solution achieves the desired improvements over
the BHMC model