Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast methods for denoising matrix completion formulations, with
  applications to robust seismic data interpolation   Recent SVD-free matrix factorization formulations have enabled rank
minimization for systems with millions of rows and columns, paving the way for
matrix completion in extremely large-scale applications, such as seismic data
interpolation.
  In this paper, we consider matrix completion formulations designed to hit a
target data-fitting error level provided by the user, and propose an algorithm
called LR-BPDN that is able to exploit factorized formulations to solve the
corresponding optimization problem. Since practitioners typically have strong
prior knowledge about target error level, this innovation makes it easy to
apply the algorithm in practice, leaving only the factor rank to be determined.
  Within the established framework, we propose two extensions that are highly
relevant to solving practical challenges of data interpolation. First, we
propose a weighted extension that allows known subspace information to improve
the results of matrix completion formulations. We show how this weighting can
be used in the context of frequency continuation, an essential aspect to
seismic data interpolation. Second, we propose matrix completion formulations
that are robust to large measurement errors in the available data.
  We illustrate the advantages of LR-BPDN on the collaborative filtering
problem using the MovieLens 1M, 10M, and Netflix 100M datasets. Then, we use
the new method, along with its robust and subspace re-weighted extensions, to
obtain high-quality reconstructions for large scale seismic interpolation
problems with real data, even in the presence of data contamination.

14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat