Hierarchical Clustering Beyond the Worst-Case

Vincent Cohen-Addad, LIP6, UPMC, Sorbonne Université
Wednesday, May 16th, 2018, 11h, salle 26-00/101, Campus Jussieu
Abstract
Hiererachical clustering, that is computing a recursive partitioning of a dataset to obtain clusters at increasingly finer granularity is a fundamental problem in data analysis. Although hierarchical clustering has mostly been studied through procedures such as linkage algorithms, or top-down heuristics, rather than as optimization problems, Dasgupta recently proposed an objective function for hierarchical clustering and initiated a line of work developing algorithms that explicitly optimize an objective. In this paper, we consider a fairly general random graph model for hierarchical clustering, called the hierarchical stochastic block model (HSBM), and show that in certain regimes the SVD approach of McSherry combined with specific linkage methods results in a clustering that give an O(1) approximation to Dasgupta’s cost function. Finally, we report empirical evaluation on synthetic and real-world data showing that our proposed SVD-based method does indeed achieve a better cost than other widely-used heurstics and also results in a better classification accuracy when the underlying problem was that of multi-class classification.
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