Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hanson-Wright inequality in Hilbert spaces with application to $K$-means
  clustering for non-Euclidean data   We derive a dimension-free Hanson-Wright inequality for quadratic forms of
independent sub-gaussian random variables in a separable Hilbert space. Our
inequality is an infinite-dimensional generalization of the classical
Hanson-Wright inequality for finite-dimensional Euclidean random vectors. We
illustrate an application to the generalized $K$-means clustering problem for
non-Euclidean data. Specifically, we establish the exponential rate of
convergence for a semidefinite relaxation of the generalized $K$-means, which
together with a simple rounding algorithm imply the exact recovery of the true
clustering structure.

25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg