Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From graph cuts to isoperimetric inequalities: Convergence rates of
  Cheeger cuts on data clouds   In this work we study statistical properties of graph-based clustering
algorithms that rely on the optimization of balanced graph cuts, the main
example being the optimization of Cheeger cuts. We consider proximity graphs
built from data sampled from an underlying distribution supported on a generic
smooth compact manifold $M$. In this setting, we obtain high probability
convergence rates for both the Cheeger constant and the associated Cheeger cuts
towards their continuum counterparts. The key technical tools are careful
estimates of interpolation operators which lift empirical Cheeger cuts to the
continuum, as well as continuum stability estimates for isoperimetric problems.
To our knowledge the quantitative estimates obtained here are the first of
their kind.

18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
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The categories of this paper are: eess
10
The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con