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

Date and Time: Thursday, May 04, 2006, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Jiří Matoušek (Charles Univ., Prague)

On the Johnson-Lindenstrauss flattening lemma

The Johnson-Lindenstrauss lemma is the following important and counter-intuitive fact: Any set of n points in the n-dimensional Euclidean space can be mapped to the Euclidean space of dimension only O(log n) almost isometrically; that is, so that no distance is distorted by more than 1%. A suitable mapping is given by a random projection. We discuss a somewhat streamlined approach to the proof, which subsumes some variants of the lemma recently treated in the literature. Most of the time we will pass from tail estimates to the moment generating function and back; this kind of gymnastics may be useful in other contexts as well.

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