Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rademacher Chaos, Random Eulerian Graphs and The Sparse
  Johnson-Lindenstrauss Transform   The celebrated dimension reduction lemma of Johnson and Lindenstrauss has
numerous computational and other applications. Due to its application in
practice, speeding up the computation of a Johnson-Lindenstrauss style
dimension reduction is an important question. Recently, Dasgupta, Kumar, and
Sarlos (STOC 2010) constructed such a transform that uses a sparse matrix. This
is motivated by the desire to speed up the computation when applied to sparse
input vectors, a scenario that comes up in applications. The sparsity of their
construction was further improved by Kane and Nelson (ArXiv 2010).
  We improve the previous bound on the number of non-zero entries per column of
Kane and Nelson from $O(1/\epsilon \log(1/\delta)\log(k/\delta))$ (where the
target dimension is $k$, the distortion is $1\pm \epsilon$, and the failure
probability is $\delta$) to $$ O\left({1\over\epsilon}
\left({\log(1/\delta)\log\log\log(1/\delta) \over
\log\log(1/\delta)}\right)^2\right). $$
  We also improve the amount of randomness needed to generate the matrix. Our
results are obtained by connecting the moments of an order 2 Rademacher chaos
to the combinatorial properties of random Eulerian multigraphs. Estimating the
chance that a random multigraph is composed of a given number of node-disjoint
Eulerian components leads to a new tail bound on the chaos. Our estimates may
be of independent interest, and as this part of the argument is decoupled from
the analysis of the coefficients of the chaos, we believe that our methods can
be useful in the analysis of other chaoses.

26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int