Meila (2018) introduces an optimization based method called the Sublevel Set method, to guarantee that a clustering is nearly optimal and "approximately correct" without relying on any assumptions about the distribution that generated the data. This paper extends the Sublevel Set method to the cost-based hierarchical clustering paradigm proposed by Dasgupta (2016).
@article{arxiv.2006.10274,
title = {Guarantees for Hierarchical Clustering by the Sublevel Set method},
author = {Marina Meila},
journal= {arXiv preprint arXiv:2006.10274},
year = {2020}
}