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Title: Polylogarithmic Sketches for Clustering
Given n points in 𝓁_p^d, we consider the problem of partitioning points into k clusters with associated centers. The cost of a clustering is the sum of p-th powers of distances of points to their cluster centers. For p ∈ [1,2], we design sketches of size poly(log(nd),k,1/ε) such that the cost of the optimal clustering can be estimated to within factor 1+ε, despite the fact that the compressed representation does not contain enough information to recover the cluster centers or the partition into clusters. This leads to a streaming algorithm for estimating the clustering cost with space poly(log(nd),k,1/ε). We also obtain a distributed memory algorithm, where the n points are arbitrarily partitioned amongst m machines, each of which sends information to a central party who then computes an approximation of the clustering cost. Prior to this work, no such streaming or distributed-memory algorithm was known with sublinear dependence on d for p ∈ [1,2).  more » « less
Award ID(s):
2002201
NSF-PAR ID:
10529463
Author(s) / Creator(s):
;
Editor(s):
Bojańczyk, Mikołaj; Merelli, Emanuela; Woodruff, David P
Publisher / Repository:
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Date Published:
Volume:
229
ISSN:
1868-8969
ISBN:
978-3-95977-235-8
Page Range / eLocation ID:
229-229
Subject(s) / Keyword(s):
sketching clustering Theory of computation → Sketching and sampling
Format(s):
Medium: X Size: 20 pages; 847506 bytes Other: application/pdf
Size(s):
20 pages 847506 bytes
Right(s):
Creative Commons Attribution 4.0 International license; info:eu-repo/semantics/openAccess
Sponsoring Org:
National Science Foundation
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