Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, December 13, 2018, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Vaggos Chatziafratis (Stanford)

Hierarchical Clustering better than Average-Linkage

Hierarchical Clustering (HC) is a widely studied problem in exploratory data analysis, usually tackled by simple agglomerative procedures like average-linkage, single-linkage or complete-linkage. In this paper we focus on two objectives, introduced recently to give insight into the performance of average-linkage clustering: a similarity based HC objective proposed by [Moseley and Wang, 2017] and a dissimilarity based HC objective proposed by [Cohen-Addad et al., 2018]. In both cases, we present tight counterexamples showing that average-linkage cannot obtain better than 1/3 and 2/3 approximations respectively (in the worst-case), settling an open question raised in [Moseley and Wang, 2017]. This matches the approximation ratio of a random solution, raising a natural question: can we beat average-linkage for these objectives? We answer this in the affirmative, giving two new algorithms based on semidefinite programming with provably better guarantees. Joint work with Moses Charikar and Rad Niazadeh (Stanford). To appear in SODA 2019.

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