  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.
