Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differentially private $k$-means clustering via exponential mechanism
  and max cover   We introduce a new $(\epsilon_p, \delta_p)$-differentially private algorithm
for the $k$-means clustering problem. Given a dataset in Euclidean space, the
$k$-means clustering problem requires one to find $k$ points in that space such
that the sum of squares of Euclidean distances between each data point and its
closest respective point among the $k$ returned is minimised. Although there
exist privacy-preserving methods with good theoretical guarantees to solve this
problem [Balcan et al., 2017; Kaplan and Stemmer, 2018], in practice it is seen
that it is the additive error which dictates the practical performance of these
methods. By reducing the problem to a sequence of instances of maximum coverage
on a grid, we are able to derive a new method that achieves lower additive
error then previous works. For input datasets with cardinality $n$ and diameter
$\Delta$, our algorithm has an $O(\Delta^2 (k \log^2 n
\log(1/\delta_p)/\epsilon_p + k\sqrt{d \log(1/\delta_p)}/\epsilon_p))$ additive
error whilst maintaining constant multiplicative error. We conclude with some
experiments and find an improvement over previously implemented work for this
problem.

3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat