Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weighted Cheeger and Buser Inequalities, with Applications to Clustering
  and Cutting Probability Densities   In this paper, we show how sparse or isoperimetric cuts of a probability
density function relate to Cheeger cuts of its principal eigenfunction, for
appropriate definitions of `sparse cut' and `principal eigenfunction'.
  We construct these appropriate definitions of sparse cut and principal
eigenfunction in the probability density setting. Then, we prove Cheeger and
Buser type inequalities similar to those for the normalized graph Laplacian of
Alon-Milman. We demonstrate that no such inequalities hold for most prior
definitions of sparse cut and principal eigenfunction. We apply this result to
generate novel algorithms for cutting probability densities and clustering
data, including a principled variant of spectral clustering.

24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph