Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perturbation Bounds for Procrustes, Classical Scaling, and
  Trilateration, with Applications to Manifold Learning   One of the common tasks in unsupervised learning is dimensionality reduction,
where the goal is to find meaningful low-dimensional structures hidden in
high-dimensional data. Sometimes referred to as manifold learning, this problem
is closely related to the problem of localization, which aims at embedding a
weighted graph into a low-dimensional Euclidean space. Several methods have
been proposed for localization, and also manifold learning. Nonetheless, the
robustness property of most of them is little understood. In this paper, we
obtain perturbation bounds for classical scaling and trilateration, which are
then applied to derive performance bounds for Isomap, Landmark Isomap, and
Maximum Variance Unfolding. A new perturbation bound for procrustes analysis
plays a key role.

20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex