Skip to main content

A General Framework for a Principled Hierarchical Visualization of Multivariate Data

  • Conference paper
  • First Online:
Intelligent Data Engineering and Automated Learning — IDEAL 2002 (IDEAL 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2412))

Abstract

We present a general framework for interactive visualization and analysis of multi-dimensional data points. The proposed model is a hierarchical extension of the latent trait family of models developed in [4] as a generalization of GTM to noise models from the exponential family of distributions. As some members of the exponential family of distributions are suitable for modeling discrete observations, we give a brief example of using our methodology in interactive visualization and semantic discovery in a corpus of text-based documents. We also derive formulas for computing local magnification factors of latent trait projection manifolds.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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.

References

  1. C. Bishop, M. Svensén, and C. Williams, “Magnification factors for the SOM and GTM algorithms,” in Proceedings 1997 Workshop on Self-Organizing Maps, Helsinki, Finland, 1997.

    Google Scholar 

  2. C. Bishop and M. E. Tipping, “A Hierarchic Latent Variable Model for data Visualization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(3), pp. 281–293, 1998.

    Article  Google Scholar 

  3. M. I. Jordan, “Hierarchical Mixture of Experts and the EM Algorithm”. Neural Computation, (6), pp. 181–214, 1994.

    Article  Google Scholar 

  4. A. Kabán and M. Girolami, “A combined latent class and trait model for the analysis and visualization of discrete data,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(8), pp. 859–872, 2001.

    Article  Google Scholar 

  5. T. Kohonen, Self-organized formation of topographically correct feature maps. Biological Cybernetics, vol. 43, pp. 59–69, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  6. P. McCullagh and L. Nelder, Generalized Linear Models. Chapman and Hall, 1985.

    Google Scholar 

  7. R. Miikkulainen, Script recognition with hierarchical feature maps Connection Science, vol. 2, pp. 83–101, 1990.

    Google Scholar 

  8. Sahami, Using Machine Learning to Improve Information Access, PhD Thesis, Stanford University, 1998.

    Google Scholar 

  9. P. Tiňo and I. Nabney, “Constructing localized non-linear projection manifolds in a principled way: hierarchical generative topographic mapping,” IEEE Transactions on Pattern Analysis and Machine Intelligence, in print.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kabán, A., Tiňo, P., Girolami, M. (2002). A General Framework for a Principled Hierarchical Visualization of Multivariate Data. In: Yin, H., Allinson, N., Freeman, R., Keane, J., Hubbard, S. (eds) Intelligent Data Engineering and Automated Learning — IDEAL 2002. IDEAL 2002. Lecture Notes in Computer Science, vol 2412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45675-9_78

Download citation

  • DOI: https://doi.org/10.1007/3-540-45675-9_78

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44025-3

  • Online ISBN: 978-3-540-45675-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics