Exact and Approximate Hierarchical Clustering Using A*

• URL: http://arxiv.org/abs/2104.07061v1
• Date: Wed, 14 Apr 2021 18:15:27 GMT
• Title: Exact and Approximate Hierarchical Clustering Using A*
• Authors: Craig S. Greenberg, Sebastian Macaluso, Nicholas Monath, Avinava Dubey, Patrick Flaherty, Manzil Zaheer, Amr Ahmed, Kyle Cranmer, Andrew McCallum
• Abstract summary: We introduce a new approach based on A* search for clustering. We overcome the prohibitively large search space by combining A* with a novel emphtrellis data structure. We empirically demonstrate that our method achieves substantially higher quality results than baselines for a particle physics use case and other clustering benchmarks.
• Score: 51.187990314731344
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Hierarchical clustering is a critical task in numerous domains. Many approaches are based on heuristics and the properties of the resulting clusterings are studied post hoc. However, in several applications, there is a natural cost function that can be used to characterize the quality of the clustering. In those cases, hierarchical clustering can be seen as a combinatorial optimization problem. To that end, we introduce a new approach based on A* search. We overcome the prohibitively large search space by combining A* with a novel \emph{trellis} data structure. This combination results in an exact algorithm that scales beyond previous state of the art, from a search space with $10^{12}$ trees to $10^{15}$ trees, and an approximate algorithm that improves over baselines, even in enormous search spaces that contain more than $10^{1000}$ trees. We empirically demonstrate that our method achieves substantially higher quality results than baselines for a particle physics use case and other clustering benchmarks. We describe how our method provides significantly improved theoretical bounds on the time and space complexity of A* for clustering.

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