Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pointwise convergence of the Lloyd algorithm in higher dimension   We establish the pointwise convergence of the iterative Lloyd algorithm, also
known as $k$-means algorithm, when the quadratic quantization error of the
starting grid (with size $N\ge 2$) is lower than the minimal quantization error
with respect to the input distribution is lower at level $N-1$. Such a protocol
is known as the splitting method and allows for convergence even when the input
distribution has an unbounded support. We also show under very light assumption
that the resulting limiting grid still has full size $N$. These results are
obtained without continuity assumption on the input distribution. A variant of
the procedure taking advantage of the asymptotic of the optimal quantizer
radius is proposed which always guarantees the boundedness of the iterated
grids.

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The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
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The categories of this paper are: eess