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Bregman Divergences and Multi-dimensional Scaling

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Advances in Neuro-Information Processing (ICONIP 2008)

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

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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.

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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 

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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
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  2. Colin Fyfe
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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

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© 2009 Springer-Verlag Berlin Heidelberg

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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

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  • 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)

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