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UID:www.tcs.tifr.res.in/event/397
DTSTAMP:20230914T125923Z
SUMMARY:A Johnson-Lindenstrauss Lemma With Independent Subgaussian Projecti
on Coefficients
DESCRIPTION:Speaker: Swagato Sanyal\n\nAbstract: \nThe Johnson-Lindenstrau
ss lemma asserts that any n-point set in any Euclidean space can be mapped
to a Euclidean space of dimension $k= O(\\epsilon^{-2} \\log n)$ so that
all distances are preserved upto a multiplicative factor between $(1 - \\e
psilon)$ and $(1+\\epsilon)$. There are several proofs of $JL Lemma$\, the
notable ones being by Indyk and Motwani\, Dasgupta and Gupta\, Achlioptas
. All these proofs obtain such a mapping as a linear map $R^n -> R^k$ wi
th a suitable random matrix. In this talk I intend to present a portion of
a 2008 paper by Matoušek\, where the author gives a simple and self-cont
ained proof of the $JL-lemma$ which subsumes several of the earlier proofs
. The paper uses a distribution on $n$ by $k$ matrices where the entries a
re independent random variables with mean $0$ and bounded variance\, and w
ith a uniform subgaussian tail. The distributions used by Indyk-Motwani an
d Achlioptas turn out to both fall in this category.\n
URL:https://www.tcs.tifr.res.in/web/events/397
DTSTART;TZID=Asia/Kolkata:20130823T160000
DTEND;TZID=Asia/Kolkata:20130823T173000
LOCATION:D-405 (D-Block Seminar Room)
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