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Foundations of Comparison-Based Hierarchical Clustering

2 November 2018
Debarghya Ghoshdastidar
Michaël Perrot
U. V. Luxburg
ArXiv (abs)PDFHTML
Abstract

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 iii and jjj are more similar than objects kkk and lll." 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 provide statistical guarantees for the different methods under a planted hierarchical partition model. We also empirically demonstrate the performance of the proposed approaches on several datasets.

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