Motivated by applications to classification problems on metric data, we study Weighted Metric Clustering problem: given a metric d over n points and a k x k symmetric matrix A with nonnegative entries, the goal is to find a kpartition of these points into clusters C1,...,Ck, while minimizing the sum of A[i,j] * d(u,v) over all pairs of clusters Ci and Cj and all pairs of points u from Ci and v from Cj. Specific choices of A lead to Weighted Metric Clustering capturing wellstudied graph partitioning problems in metric spaces, such as MinUncut, MinkSum, MinkCut, and more.Our main result is that Weighted Metric Clustering admits a polynomialtime approximation scheme (PTAS). Our algorithm handles all the above problems using the SheraliAdams linear programming relaxation. This subsumes several prior works, unifies many of the techniques for various metric clustering objectives, and yields a PTAS for several new problems, including metric clustering on manifolds and a new family of hierarchical clustering objectives. Our experiments on the hierarchical clustering objective show that it better captures the groundtruth structural information compared to the popular Dasgupta's objective.
We introduce a novel criterion in clustering that seeks clusters with limited
 Award ID(s):
 1760102
 NSFPAR ID:
 10075710
 Publisher / Repository:
 Wiley Blackwell (John Wiley & Sons)
 Date Published:
 Journal Name:
 Networks
 Volume:
 73
 Issue:
 2
 ISSN:
 00283045
 Page Range / eLocation ID:
 p. 170186
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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