Multigrid multidimensional scaling

M. M. Bronstein, A. M. Bronstein, R. Kimmel, I. Yavneh

Research output: Contribution to journalArticlepeer-review

Abstract

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. In 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.

Original languageEnglish
Pages (from-to)149-171
Number of pages23
JournalNumerical Linear Algebra with Applications
Volume13
Issue number2-3
DOIs
StatePublished - Mar 2006
Externally publishedYes

Keywords

  • BFGS
  • Bending-invariant canonical form
  • Dimensionality reduction
  • Face recognition
  • Isometric embedding
  • Multidimensional scaling
  • Multigrid
  • Multiresolution
  • SMACOF

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