We present a new way to summarize and select mixture models via the hierarchical clustering tree (dendrogram) of 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：我们提出了一种通过过拟合潜在混合测度的层次聚类树（树状图）来总结和选择混合模型的新方法。该方法弥合了凝聚层次聚类与混合建模的鸿沟。树状图的构建源于混合测度收敛理论，因此即使模型参数仅具有弱可辨识性，我们也能从树中一致地选择真实混合成分数量，并获得参数估计的逐点最优收敛速率。理论上，该方法阐明了层次聚类中最优簇数的选择准则；实践中，与传统混合模型总结方式相比，树状图揭示了更多关于子群体层次结构的信息。我们通过多项仿真研究验证了理论结果，并将该方法应用于单细胞RNA序列分析。