Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: k-variates++: more pluses in the k-means++   k-means++ seeding has become a de facto standard for hard clustering
algorithms. In this paper, our first contribution is a two-way generalisation
of this seeding, k-variates++, that includes the sampling of general densities
rather than just a discrete set of Dirac densities anchored at the point
locations, and a generalisation of the well known Arthur-Vassilvitskii (AV)
approximation guarantee, in the form of a bias+variance approximation bound of
the global optimum. This approximation exhibits a reduced dependency on the
"noise" component with respect to the optimal potential --- actually
approaching the statistical lower bound. We show that k-variates++ reduces to
efficient (biased seeding) clustering algorithms tailored to specific
frameworks; these include distributed, streaming and on-line clustering, with
direct approximation results for these algorithms. Finally, we present a novel
application of k-variates++ to differential privacy. For either the specific
frameworks considered here, or for the differential privacy setting, there is
little to no prior results on the direct application of k-means++ and its
approximation bounds --- state of the art contenders appear to be significantly
more complex and / or display less favorable (approximation) properties. We
stress that our algorithms can still be run in cases where there is \textit{no}
closed form solution for the population minimizer. We demonstrate the
applicability of our analysis via experimental evaluation on several domains
and settings, displaying competitive performances vs state of the art.

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The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat