Bayesian hierarchical mixture clustering (BHMC) improves traditionalBayesian hierarchical clustering by replacing conventional Gaussian-to-Gaussian kernels with a Hierarchical Dirichlet Process Mixture Model(HDPMM) for parent-to-child diffusion in the generative process. However,BHMC may produce trees with high nodal variance, indicating weak separation between nodes at higher levels. To address this issue, we employ Posterior Regularization, which imposes max-margin constraints on nodes at every level to enhance cluster separation. We illustrate how to apply PR toBHMC and demonstrate its effectiveness in improving the BHMC model.

翻译：贝叶斯分层混合聚类(Bayesian hierarchical mixture clustering, BHMC)改进了传统贝叶斯分层聚类，在生成过程中用层次狄利克雷过程混合模型(HDPMM)替代传统的高斯-高斯核，实现父节点到子节点的扩散。然而，BHMC可能产生具有高节点方差的树结构，表明高层级节点之间的分离度较弱。为解决这一问题，我们采用后验正则化方法，对每一层级节点施加最大间隔约束以增强聚类分离度。我们阐述了如何将后验正则化应用于BHMC，并证明了其在改进BHMC模型方面的有效性。