  The intricacies inherent in contemporary real datasets demand more advanced
statistical models to effectively address complex challenges. In this article
we delve into problems related to identifying clusters across related groups,
when additional covariate information is available. We formulate a novel
Bayesian nonparametric approach based on mixture models, integrating ideas from
the hierarchical Dirichlet process and "single-atoms" dependent Dirichlet
process. The proposed method exhibits exceptional generality and flexibility,
accommodating both continuous and discrete covariates through the utilization
of appropriate kernel functions. We construct a robust and efficient Markov
chain Monte Carlo (MCMC) algorithm involving data augmentation to tackle the
intractable normalized weights. The versatility of the proposed model extends
our capability to discern the relationship between covariates and clusters.
Through testing on both simulated and real-world datasets, our model
demonstrates its capacity to identify meaningful clusters across groups,
providing valuable insights for a spectrum of applications.
