Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Manifold Repairing, Reconstruction and Denoising from Scattered Data in
  High-Dimension   We consider a problem of great practical interest: the repairing and recovery
of a low-dimensional manifold embedded in high-dimensional space from noisy
scattered data. Suppose that we observe a point cloud sampled from the
low-dimensional manifold, with noise, and let us assume that there are holes in
the data. Can we recover missing information inside the holes? While in
low-dimension the problem was extensively studied, manifold repairing in high
dimension is still an open problem. We introduce a new approach, called
Repairing Manifold Locally Optimal Projection (R-MLOP), that expands the MLOP
method introduced by Faigenbaum-Golovin et al. in 2020, to cope with manifold
repairing in low and high-dimensional cases. The proposed method can deal with
multiple holes in a manifold. We prove the validity of the proposed method, and
demonstrate the effectiveness of our approach by considering different manifold
topologies, for single and multiple holes repairing, in low and high
dimensions.

17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph