Foundations of Comparison-Based Hierarchical Clustering

Debarghya Ghoshdastidar; Michaël Perrot; Ulrike von Luxburg

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arXiv · 1811.00928

Foundations of Comparison-Based Hierarchical Clustering

Debarghya Ghoshdastidar·Michaël Perrot·Ulrike von Luxburg

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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 $i$ 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 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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BibTeX RIS

Debarghya Ghoshdastidar, Michaël Perrot, Ulrike von Luxburg. 2018-11-02. Foundations of Comparison-Based Hierarchical Clustering. https://arxiv.org/abs/1811.00928

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