Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Bregman Divergences and Multi-dimensional Scaling

  • Conference paper
Advances in Neuro-Information Processing (ICONIP 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5507))

Included in the following conference series:

Abstract

We discuss Bregman divergences and the very close relationship between a class of these divergences and the regular family of exponential distributions before applying them to various topology preserving dimension reducing algorithms. We apply these to multidimensional scaling (MDS) and show the effect of different Bregman divergences. In particular we derive a mapping similar to the Sammon mapping. We apply these methods to face identification.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Azoury, K.S., Warmouth, M.K.: Relative loss bounds for on-line density estimation with the exponential family of distributions. Machine Learning (43), 211–246 (2001)

    Google Scholar 

  2. Banerjee, A., Meruga, S., Dhillon, I., Ghosh, J.: Clustering with bregman divergences. Journal of Machine Learning Research 6, 1705–1749 (2005)

    MathSciNet  MATH  Google Scholar 

  3. Collins, M., Dasgupta, S., Shapire, R.E.: A generalization of principal component analysis to the exponential family. In: NIPS 14 (2002)

    Google Scholar 

  4. Lee, J.A., Verleysen, M.: Nonlinear Dimensionality Reduction. Springer, Heidelberg (2007)

    Book  MATH  Google Scholar 

  5. Neilsen, F., Boissonnat, J.-D., Nock, R.: Bregman voronoi diagrams: Properties, algorithms and applications (submitted, 2007)

    Google Scholar 

  6. Neilsen, F., Boissonnat, J.-D., Nock, R.: On bregman voronoi diagrams. In: ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 746–755 (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Southern Taiwan University, Tainan, Taiwan

    Pei Ling Lai

  2. University of the West of Scotland, UK

    Colin Fyfe

Authors
  1. Pei Ling Lai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Colin Fyfe
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Network Design and Research Center, Kyushu Institute of Technology,, 680-4, Kawazu, Iizuka,, 820-8502, Fukuoka, Japan

    Mario Köppen

  2. Knowledge Engineering and Discovery Research Institute (KEDRI), School of Computing and Mathematical Sciences, Auckland University of Technology, 350 Queen Street, 10110, Auckland, New Zealand

    Nikola Kasabov

  3. Department of Electrical and Computer Engineering, Robotics Laboratory, Auckland University of Technology, 38 Princes Street,, 1142, Auckland, New Zealand

    George Coghill

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lai, P.L., Fyfe, C. (2009). Bregman Divergences and Multi-dimensional Scaling. In: Köppen, M., Kasabov, N., Coghill, G. (eds) Advances in Neuro-Information Processing. ICONIP 2008. Lecture Notes in Computer Science, vol 5507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03040-6_114

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03040-6_114

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03039-0

  • Online ISBN: 978-3-642-03040-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation