---
_id: '18318'
abstract:
- lang: eng
  text: "Multidimensional scaling (MDS) is a generic name for a family of algorithms
    that construct a configuration of points in a target metric space from information
    about inter-point distances measured in some other metric space. Large-scale MDS
    problems often occur in data analysis, representation and visualization. Solving
    such problems efficiently is of key importance in many applications.\r\nIn this
    paper we present a multigrid framework for MDS problems. We demonstrate the performance
    of our algorithm on dimensionality reduction and isometric embedding problems,
    two classical problems requiring efficient large-scale MDS. Simulation results
    show that the proposed approach significantly outperforms conventional MDS algorithms."
article_processing_charge: No
article_type: original
author:
- first_name: M. M.
  full_name: Bronstein, M. M.
  last_name: Bronstein
- first_name: Alexander
  full_name: Bronstein, Alexander
  id: 58f3726e-7cba-11ef-ad8b-e6e8cb3904e6
  last_name: Bronstein
  orcid: 0000-0001-9699-8730
- first_name: R.
  full_name: Kimmel, R.
  last_name: Kimmel
- first_name: I.
  full_name: Yavneh, I.
  last_name: Yavneh
citation:
  ama: Bronstein MM, Bronstein AM, Kimmel R, Yavneh I. Multigrid multidimensional
    scaling. <i>Numerical Linear Algebra with Applications</i>. 2006;13(2-3):149-171.
    doi:<a href="https://doi.org/10.1002/nla.475">10.1002/nla.475</a>
  apa: Bronstein, M. M., Bronstein, A. M., Kimmel, R., &#38; Yavneh, I. (2006). Multigrid
    multidimensional scaling. <i>Numerical Linear Algebra with Applications</i>. Wiley.
    <a href="https://doi.org/10.1002/nla.475">https://doi.org/10.1002/nla.475</a>
  chicago: Bronstein, M. M., Alex M. Bronstein, R. Kimmel, and I. Yavneh. “Multigrid
    Multidimensional Scaling.” <i>Numerical Linear Algebra with Applications</i>.
    Wiley, 2006. <a href="https://doi.org/10.1002/nla.475">https://doi.org/10.1002/nla.475</a>.
  ieee: M. M. Bronstein, A. M. Bronstein, R. Kimmel, and I. Yavneh, “Multigrid multidimensional
    scaling,” <i>Numerical Linear Algebra with Applications</i>, vol. 13, no. 2–3.
    Wiley, pp. 149–171, 2006.
  ista: Bronstein MM, Bronstein AM, Kimmel R, Yavneh I. 2006. Multigrid multidimensional
    scaling. Numerical Linear Algebra with Applications. 13(2–3), 149–171.
  mla: Bronstein, M. M., et al. “Multigrid Multidimensional Scaling.” <i>Numerical
    Linear Algebra with Applications</i>, vol. 13, no. 2–3, Wiley, 2006, pp. 149–71,
    doi:<a href="https://doi.org/10.1002/nla.475">10.1002/nla.475</a>.
  short: M.M. Bronstein, A.M. Bronstein, R. Kimmel, I. Yavneh, Numerical Linear Algebra
    with Applications 13 (2006) 149–171.
date_created: 2024-10-15T11:12:06Z
date_published: 2006-03-01T00:00:00Z
date_updated: 2024-11-12T08:45:09Z
day: '01'
doi: 10.1002/nla.475
extern: '1'
intvolume: '        13'
issue: 2-3
language:
- iso: eng
month: '03'
oa_version: None
page: 149-171
publication: Numerical Linear Algebra with Applications
publication_identifier:
  eissn:
  - 1099-1506
  issn:
  - 1070-5325
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Multigrid multidimensional scaling
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 13
year: '2006'
...