Entropy-based bounds on dimension reduction in L1

Research output: Contribution to journalArticle

Abstract

We show that for every large enough integer N, there exists an N-point subset of L 1 such that for every D > 1, embedding it into ℓ 1 d with distortion D requires dimension d at least NΩ (1/D2), and that for every e{open} > 0 and large enough integer N, there exists an N-point subset of L 1 such that embedding it into ℓ 1 d with distortion 1 + e{open} requires dimension d at least NΩ (1/D2)). These results were previously proven by Brinkman and Charikar [JACM, 2005] and by Andoni, Charikar, Neiman and Nguyen [FOCS 2011]. We provide an alternative and arguably more intuitive proof based on an entropy argument.

Original languageEnglish (US)
Pages (from-to)825-832
Number of pages8
JournalIsrael Journal of Mathematics
Volume195
Issue number2
DOIs
StatePublished - Jun 2013

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Dimension Reduction
Entropy
Integer
Subset
Intuitive
Alternatives

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Entropy-based bounds on dimension reduction in L1 . / Regev, Oded.

In: Israel Journal of Mathematics, Vol. 195, No. 2, 06.2013, p. 825-832.

Research output: Contribution to journalArticle

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