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Accepted Paper at KDD 2023

Connecting the Dots — Density-Connectivity Distance unifies DBSCAN, k-Center and Spectral Clustering



Anna Beer, Andrew Draganov, Ellen Hohma, Philipp Jahn, Christian M.M. Frey, Ira Assent


29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD 2023),
06–10 August 2023, Long Beach, CA, USA



Despite the popularity of density-based clustering, its procedural definition makes it difficult to analyze compared to clustering methods that minimize a loss function. In this paper, we reformulate DBSCAN through a clean objective function by introducing the density-connectivity distance (dc-dist), which captures the essence of density-based clusters by endowing the minimax distance with the concept of density. This novel ultrametric allows us to show that DBSCAN, k-center, and spectral clustering are equivalent in the space given by the dc-dist, despite these algorithms being perceived as fundamentally different in their respective literatures. We also verify that finding the pairwise dc-dists gives DBSCAN clusterings across all epsilon-values, simplifying the problem of parameterizing density-based clustering. We conclude by thoroughly analyzing density-connectivity and its properties -- a task that has been elusive thus far in the literature due to the lack of formal tools.