Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the minimum of the mean-squared error in 2-means clustering   We study the minimum mean-squared error for 2-means clustering when the
outcomes of the vector-valued random variable to be clustered are on two
touching spheres of unit radius in $n$-dimensional Euclidean space and the
underlying probability distribution is the normalized surface measure. For
simplicity, we only consider the asymptotics of large sample sizes and replace
empirical samples by the probability measure. The concrete question addressed
here is whether a minimizer for the mean-squared error identifies the two
individual spheres as clusters. Indeed, in dimensions $n \ge 3$, the minimum of
the mean-squared error is achieved by a partition that separates the two
spheres and has unit distance between the points in each cluster and the
respective mean. In dimension $n=2$, however, the minimizer fails to identify
the individual spheres; an optimal partition is obtained by a separating
hyperplane that does not contain the point at which the spheres touch.

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The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg