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Erschienen in:
2005 | OriginalPaper | Buchkapitel
Fast k-Means Algorithms with Constant Approximation
verfasst von : Mingjun Song, Sanguthevar Rajasekaran
Erschienen in: Algorithms and Computation
Verlag: Springer Berlin Heidelberg
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In this paper we study the
k
-means clustering problem. It is well-known that the general version of this problem is
$\mathcal{NP}$
-hard. Numerous approximation algorithms have been proposed for this problem. In this paper, we proposed three constant approximation algorithms for
k
-means clustering. The first algorithm runs in time
$O(({{k}\over{\epsilon}})^{k}nd)$
, where
k
is the number of clusters,
n
is the size of input points,
d
is dimension of attributes. The second algorithm runs in time
O
(
k
3
n
2
log
n
). This is the first algorithm for
k
-means clustering that runs in time polynomial in
n
,
k
and
d
. The run time of the third algorithm (
O
(
k
5
log
3
kd
)) is independent of
n
. Though an algorithm whose run time is independent of
n
is known for the
k
-median problem, ours is the first such algorithm for the
k
-means problem.