Oblivious dimension reduction for k -means: beyond subspaces and the Johnson-Lindenstrauss lemma

Abstract : We show that for n points in d-dimensional Euclidean space, a data oblivious random projection of the columns onto m∈ O((logk+loglogn)ε−6log1/ε) dimensions is sufficient to approximate the cost of all k-means clusterings up to a multiplicative (1±ε) factor. The previous-best upper bounds on m are O(logn· ε−2) given by a direct application of the Johnson-Lindenstrauss Lemma, and O(kε−2) given by [Cohen et al.-STOC’15].
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Conference papers
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https://hal.archives-ouvertes.fr/hal-02169563
Contributor : Vincent Cohen-Addad <>
Submitted on : Monday, July 1, 2019 - 12:25:12 PM
Last modification on : Thursday, November 21, 2019 - 10:18:56 AM

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Luca Becchetti, Marc Bury, Vincent Cohen-Addad, Fabrizio Grandoni, Chris Schwiegelshohn. Oblivious dimension reduction for k -means: beyond subspaces and the Johnson-Lindenstrauss lemma. STOC 2019 - 51st Annual ACM SIGACT Symposium on Theory of Computing, Jun 2019, Phoenix, United States. pp.1039-1050, ⟨10.1145/3313276.3316318⟩. ⟨hal-02169563⟩

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