Entropy-based bounds on dimension reduction in L-1 - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Israel Journal of Mathematics Year : 2013

Entropy-based bounds on dimension reduction in L-1

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 a"" (1) (d) with distortion D requires dimension d at least , and that for every E > > 0 and large enough integer N, there exists an N-point subset of L (1) such that embedding it into a"" (1) (d) with distortion 1 + E > requires dimension d at least ). 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.

Dates and versions

hal-01111562 , version 1 (30-01-2015)

Identifiers

Cite

Oded Regev. Entropy-based bounds on dimension reduction in L-1. Israel Journal of Mathematics, 2013, 195 (2), pp.825-832. ⟨10.1007/s11856-012-0137-6⟩. ⟨hal-01111562⟩
46 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More