In this work the authors study hierarchical clustering under quadruplet comparison framework. The authors show that single and complete linkages are inherently comparison based and propose two variants of average linkage clustering exploiting quadruplet comparison. Exact hierarchy recovery guarantee is provided under planted hierarchical partition model and empirical evaluation is provided. The meaning of the variables \mu, \delta etc are hard to interpret from the description. They have been nicely summarized (and explained) in the appendix A.1.

The authors have proposed two variants of average linkage hierarchical clustering using quadruplet comparison framework. Theoretical results of hierarchy recovery is established under a suitable model. The reviewers are in agreement that the results are new and important. The authors should incorporate the suggestions made by the reviewers to further strengthen the paper.

We address the classical problem of hierarchical clustering, but in a framework where one does not have access to a representation of the objects or their pairwise similarities. Instead, we assume that only a set of comparisons between objects is available, that is, statements of the form objects i and j are more similar than objects k and l.'' Such a scenario is commonly encountered in crowdsourcing applications. The focus of this work is to develop comparison-based hierarchical clustering algorithms that do not rely on the principles of ordinal embedding. We show that single and complete linkage are inherently comparison-based and we develop variants of average linkage.

We address the classical problem of hierarchical clustering, but in a framework where one does not have access to a representation of the objects or their pairwise similarities. Instead, we assume that only a set of comparisons between objects is available, that is, statements of the form objects i and j are more similar than objects k and l.'' Such a scenario is commonly encountered in crowdsourcing applications. The focus of this work is to develop comparison-based hierarchical clustering algorithms that do not rely on the principles of ordinal embedding. We show that single and complete linkage are inherently comparison-based and we develop variants of average linkage.