Hierarchical Clustering via Sketches and Hierarchical Correlation Clustering

Danny Vainstein, Vaggos Chatziafratis, Gui Citovsky, Anand Rajagopalan, Mohammad Mahdian, Yossi Azar

Research output: Contribution to journalConference articlepeer-review

3 Scopus citations


Recently, Hierarchical Clustering (HC) has been considered through the lens of optimization. In particular, two maximization objectives have been defined. Moseley and Wang defined the Revenue objective to handle similarity information given by a weighted graph on the data points (w.l.o.g., [0, 1] weights), while Cohen-Addad et al. defined the Dissimilarity objective to handle dissimilarity information. In this paper, we prove structural lemmas for both objectives allowing us to convert any HC tree to a tree with constant number of internal nodes while incurring an arbitrarily small loss in each objective. Although the best-known approximations are 0.585 and 0.667 respectively, using our lemmas we obtain approximations arbitrarily close to 1, if not all weights are small (i.e., there exist constants ∊, δ such that the fraction of weights smaller than δ, is at most 1 − ∊); such instances encompass many metric-based similarity instances, thereby improving upon prior work. Finally, we introduce Hierarchical Correlation Clustering (HCC) to handle instances that contain similarity and dissimilarity information simultaneously. For HCC, we provide an approximation of 0.4767 and for complementary similarity/dissimilarity weights (analogous to +/− correlation clustering), we again present nearly-optimal approximations.

Original languageEnglish
Pages (from-to)559-567
Number of pages9
JournalProceedings of Machine Learning Research
StatePublished - 2021
Event24th International Conference on Artificial Intelligence and Statistics, AISTATS 2021 - Virtual, Online, United States
Duration: 13 Apr 202115 Apr 2021


FundersFunder number
Israel Science Foundation2304/20, 1506/16


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