Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, September 29, 2011, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Sebastian Stich

The Johnson-Lindenstrauss Lemma

The Johnson-Lindenstrauss Lemma asserts that a set of n points in any Euclidean space can be mapped to an Euclidean space of dimension k=O(\epsilon^{-2} \log n) so that all distances are preserved up to a multiplicative factor between (1-\epsilon) and (1+\epsilon). Known proofs obtain such a mapping as a linear map R^n -> R^k with a suitable random matrix U. The structure of U can be surprisingly simple, e.g. independent Gaussian entries (Indyk and Motwani, 1998), independent -1,1 entries (Achlioptas 2001) and even sparse (Ailon and Chazelle 2006, Matousek 2007).

We give an overview of these results and present an elementary proof of the result obtained by Indyk and Motwani.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2024  2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login