Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Frequent Directions : Simple and Deterministic Matrix Sketching   We describe a new algorithm called Frequent Directions for deterministic
matrix sketching in the row-updates model. The algorithm is presented an
arbitrary input matrix $A \in R^{n \times d}$ one row at a time. It performed
$O(d \times \ell)$ operations per row and maintains a sketch matrix $B \in
R^{\ell \times d}$ such that for any $k < \ell$
  $\|A^TA - B^TB \|_2 \leq \|A - A_k\|_F^2 / (\ell-k)$ and $\|A -
\pi_{B_k}(A)\|_F^2 \leq \big(1 + \frac{k}{\ell-k}\big) \|A-A_k\|_F^2 $ .
  Here, $A_k$ stands for the minimizer of $\|A - A_k\|_F$ over all rank $k$
matrices (similarly $B_k$) and $\pi_{B_k}(A)$ is the rank $k$ matrix resulting
from projecting $A$ on the row span of $B_k$. We show both of these bounds are
the best possible for the space allowed. The summary is mergeable, and hence
trivially parallelizable. Moreover, Frequent Directions outperforms exemplar
implementations of existing streaming algorithms in the space-error tradeoff.

24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org