We present a new way to summarize and select mixture models via the hierarchical clustering tree (dendrogram) constructed from an overfitted latent mixing measure. Our proposed method bridges agglomerative hierarchical clustering and mixture modeling. The dendrogram's construction is derived from the theory of convergence of the mixing measures, and as a result, we can both consistently select the true number of mixing components and obtain the pointwise optimal convergence rate for parameter estimation from the tree, even when the model parameters are only weakly identifiable. In theory, it explicates the choice of the optimal number of clusters in hierarchical clustering. In practice, the dendrogram reveals more information on the hierarchy of subpopulations compared to traditional ways of summarizing mixture models. Several simulation studies are carried out to support our theory. We also illustrate the methodology with an application to single-cell RNA sequence analysis.

翻译：我们提出一种新方法，通过从过拟合潜在混合度量构建的分层聚类树（树状图）来总结和选择混合模型。该方法弥合了凝聚型分层聚类与混合建模之间的鸿沟。树状图的构建源于混合度量收敛理论，因此我们能够一致地选择真实的混合分量数量，同时从树中获得参数估计的逐点最优收敛速率——即使模型参数仅具有弱可识别性。理论上，该方法阐明了分层聚类中最优聚类数量的选择标准。实践中，与传统的混合模型总结方式相比，树状图能够揭示更多关于子种群层级结构的信息。我们通过多项仿真实验验证了理论，并将该方法应用于单细胞RNA序列分析来展示其实用性。