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REPORTS > KEYWORD > JOHNSON-LINDENSTRAUSS LEMMA:
Reports tagged with Johnson-Lindenstrauss Lemma:
TR09-121 | 22nd November 2009
Zohar Karnin, Yuval Rabani, Amir Shpilka

#### Explicit Dimension Reduction and Its Applications

We construct a small set of explicit linear transformations mapping $R^n$ to $R^{O(\log n)}$, such that the $L_2$ norm of
any vector in $R^n$ is distorted by at most $1\pm o(1)$ in at
least a fraction of $1 - o(1)$ of the transformations in the set.
Albeit the tradeoff between ... more >>>

TR10-098 | 17th June 2010
Daniel Kane, Jelani Nelson

#### A Derandomized Sparse Johnson-Lindenstrauss Transform

Revisions: 2

Recent work of [Dasgupta-Kumar-Sarl\'{o}s, STOC 2010] gave a sparse Johnson-Lindenstrauss transform and left as a main open question whether their construction could be efficiently derandomized. We answer their question affirmatively by giving an alternative proof of their result requiring only bounded independence hash functions. Furthermore, the sparsity bound obtained in ... more >>>

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