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Polylogarithmic Sketches for Clustering

Authors Moses Charikar , Erik Waingarten

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  • Theory of computation → Sketching and sampling
Keywords
  • sketching
  • clustering

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Abstract

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).

Cite As Get BibTex

Moses Charikar and Erik Waingarten. Polylogarithmic Sketches for Clustering. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 38:1-38:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ICALP.2022.38

Author Details

Moses Charikar
  • Stanford University, CA, USA
Erik Waingarten
  • Stanford University, CA, USA

Funding

  • Charikar, Moses: Supported by a Simons Investigator Award.
  • Waingarten, Erik: Supported by the National Science Foundation under Award no. 2002201.

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