Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Multidimensional Scaling

  • Heng Tao Shen
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_548

Synonyms

MDS

Definition

Multidimensional scaling (MDS) is a mathematical dimension reduction technique that best preserves the interpoint distances by analyzing gram matrix. Given any two points p i and p j in a dataset P, MSD aims to minimize the following objective function:
$$ \mathrm{Error}=\sum \left[d\left( pi, pj\right)-{d}^{\prime}\left( pi, pj\right)\right]2 $$
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Recommended Reading

  1. 1.
    Cox MF, Cox MAA. Multidimensional scaling. Boca Raton: Chapman and Hall; 2001.zbMATHGoogle Scholar
  2. 2.
    Young FW, Hamer RM. Multidimensional scaling: history, theory and applications. New York: Erlbaum; 1987.Google Scholar
  3. 3.
    Zhu X, Huang Z, Shen HT, Cheng J, Xu C. Dimensionality reduction by mixed kernel canonical correlation analysis. Pattern Recog (PR). 2012;45(8):3003–16.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Information Technology and Electrical EngineeringThe University of QueenslandBrisbaneAustralia
  2. 2.University of Electronic Science and Technology of ChinaChengduChina

Section editors and affiliations

  • Xiaofang Zhou
    • 1
  1. 1.School of Information Technology and Electrical EngineeringUniversity of QueenslandBrisbaneAustralia