Skip to main content
SpringerLink
Log in

Nonlinear Multidimensional Data Projection and Visualisation

  • Conference paper
Intelligent Data Engineering and Automated Learning (IDEAL 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2690))

Abstract

Multidimensional data projection and visualisation are becoming increasingly important and have found wide applications in many fields such as decision support, bioinformatics and web/document organisation. Various methods and algorithms have been proposed as either nonparametric or semiparametric approaches. This paper provides an overview of the subject and reviews some recent developments. Relationships among various key methods such as Sammon mapping, Neuroscale, principal curve/surface, SOM, GTM and ViSOM are analysed and their advantages and limitations are highlighted in the context of nonlinear principal component analysis and independent component analysis.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Arciniegas, I., Daniel, B., Embrechts, M.J.: Exploring Financial Crises Data with selforganising maps. In: Allinson, N., Yin, H., Allinson, L., Slack, J. (eds.) Advances in Self-Organising Maps, pp. 39–46 (2001)

    Google Scholar 

  2. Banfield, J.D., Raftery, A.E.: Ice floe identification in satellite images using mathematical morphology and clustering about principal curves. Journal of the American Statistical Association 87, 7–16 (1992)

    Article  Google Scholar 

  3. Bishop, C.M., Svensén, M., Williams, C.K.I.: GTM: The generative topographic mapping. Neural Computation 10, 215–235 (1998)

    Article  Google Scholar 

  4. Bishop, C.M., Svensén, M., Williams, C.K.I.: Magnification factors for the SOM and GTM algorithms. In: Proceedings of Workshop on Self-Organizing Maps (WSOM 1997), pp. 333–338 (1997)

    Google Scholar 

  5. Biswas, G., Jain, A.K., Dubes, R.C.: Evaluation of project algorithms. IEEE Trans. On Pattern Analysis and Machine Intelligence PAMI-3, 701–708 (1981)

    Article  Google Scholar 

  6. Burel, G.: Blind separation of sources: A nonlinear neural algorithm. Neural Networks 5, 937–947 (1992)

    Article  Google Scholar 

  7. Chang, K.-Y., Ghosh, J.: A unified model for probabilistic principal surfaces. IEEE Trans. on Pattern Analysis and Machine Intelligence PAMI-23, 22–41 (2001)

    Article  Google Scholar 

  8. Condon, E., Golden, B., Lele, S., Raghavan, S., Wasil, E.: A visualization model based on adjacency data. Decision Support systems 33, 349–362 (2002)

    Article  Google Scholar 

  9. Cox, T.F., Cox, M.A.A.: Multidimensional Scaling. Chapman & Hall, Boca Raton (1994)

    MATH  Google Scholar 

  10. De Ridder, D., Duin, R.P.W.: Sammon mapping using neural networks: a comparison. Pattern Recognition Letters 18, 1307–1316 (1997)

    Article  Google Scholar 

  11. Freeman, R., Yin, H.: Self-organising maps for hierarchical tree view document clustering using contextual information. In: Yin, H., Allinson, N.M., Freeman, R., Keane, J.A., Hubbard, S. (eds.) IDEAL 2002. LNCS, vol. 2412, pp. 123–128. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  12. Girolami, M.: Self-Organising Neural Networks: Independent Component Analysis and Blind Source Separation. Springer, Heidelberg (1999)

    Google Scholar 

  13. Haritopoulos, M., Yin, H., Allinson, N.M.: Image denoising using self-organising map –based nonlinear independent component analysis. Neural Networks 15, 1085–1098 (2002)

    Article  Google Scholar 

  14. Hastie, T., Stuetzle, W.: Principal curves. Journal of the American Statistical Association 84, 502–516 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  15. Herrmann, M., Yang, H.H.: Perspectives and limitations of self-organising maps inblind separation of source signals. In: Proc. ICONIP 1996, pp. 1211–1216 (1996)

    Google Scholar 

  16. Honkela, T., Kaski, S., Lagus, K., Kohonen, T.: WEBSOM-self-organizing maps of document collections. In: Proceedings of Workshop on Self-Organizing Maps (WSOM 1997), pp. 310–315 (1997)

    Google Scholar 

  17. Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. John Wiley &Sons, Inc. Chichester (2001)

    Book  Google Scholar 

  18. Hyvärinen, A., Pajunen, P.: Nonlinear independent component analysis: Existence and uniqueness results. Neural Networks 12, 429–439 (1999)

    Article  Google Scholar 

  19. Kaban, A., Girolami, M.: A combined latent trait class and trait model for the analysis and visualisation of discrete data. IEEE Trans. on Pattern Analysis and Machine Intelligence PAMI-23, 859–872 (2001)

    Article  Google Scholar 

  20. Karhunen, J., Joutsensalo, J.: Generalisation of principal component analysis, optimization problems, and neural networks. Neural Networks 8, 549–562 (1995)

    Article  Google Scholar 

  21. Karhunen, J., Malaroiu, S.: Local independent component analysis using clusternig. In: Proc. 1st Int. Workshop on Independent Component Analysis and Signal Separation (ICA 1999), pp. 43–48 (1999)

    Google Scholar 

  22. Kaski, S., Kohonen, T.: Exploratory data analysis by the self-organizing map: Structures of welfare and poverty in the world. In: Refenes, A.-P.N., Abu-Mostafa, Y., Moody, J., Weigend, A. (eds.) Neural Networks in Financial Engineering, pp. 498–507. World Scientific, Singapore (1996)

    Google Scholar 

  23. Kegl, B., Krzyzak, A., Linder, T., Zeger, K.: A polygonal line algorithm for constructing principal curves. In: NIPS-WS 1996, vol. 11, pp. 501–507 (1998)

    Google Scholar 

  24. Kohonen, T.: Self-organised formation of topologically correct feature map. Biological Cybernetics 43, 56–69 (1982)

    Article  MathSciNet  Google Scholar 

  25. Kohonen, T.: Self-Organising Maps, 2nd edn. Springer, Berlin (1995)

    Google Scholar 

  26. Kraaijveld, M.A., Mao, J., Jain, A.K.: A nonlinear projection method based on Kohonen’s topology preserving maps. IEEE Trans. Neural Networks 6, 548–559 (1995)

    Article  Google Scholar 

  27. Kramer, M.A.: Nonlinear principal component analysis using autoassociative neural networks. AICHE Journal 37, 233–243 (1991)

    Article  Google Scholar 

  28. LeBlanc, M., Tibshirani, R.J.: Adaptive principal surfaces. J. Amer. Statist. Assoc. 89, 53–64 (1994)

    Article  MATH  Google Scholar 

  29. Lee, R.C.T., Slagle, J.R., Blum, H.: A triangulation method for the sequential mapping of points from n-space to two-space. IEEE Trans. on Computers 27, 288–292 (1977)

    Article  Google Scholar 

  30. Lee, T.-W.: Independent Component Analysis: Theory and Applications. Kluwer Academic, Dordrecht (1998)

    MATH  Google Scholar 

  31. Lee, T.-W., Koehler, B.-U., Orglmeister, R.: Blind source separation of nonlinear mixing models. In: Proc. IEEE Workshop on Neural Networks for Signal Processing (NNSP 1997), pp. 406–415 (1997)

    Google Scholar 

  32. Lee, T.-W., Lewicki, M.-S., Sejnowski, T.-J.: Unsupervised Classification with Non- Gaussian Mixture Models using ICA. Advances in Neural Information Processing Systems 11, 508–514 (1999)

    Google Scholar 

  33. Lowe, D., Tipping, M.E.: Feed-forward neural networks and topographic mappings for exploratory data analysis. Neural Computing and Applications 4, 83–95 (1996)

    Article  Google Scholar 

  34. Malthouse, E.C.: Limitations of nonlinear PCA as performed with generic neural networks. IEEE Trans. Neural Networks 9, 165–173 (1998)

    Article  Google Scholar 

  35. Mao, J., Jain, A.K.: Artificial Neural Networks for Feature Extraction and Multivariate Data Projection. IEEE Trans. on Neural Networks 6, 296–317 (1995)

    Article  Google Scholar 

  36. Mulier, F., Cherkassky, V.: Self-organisation as an iterative kernel smoothing process. Neural Computation 7, 1165–1177 (1995)

    Article  Google Scholar 

  37. Oja, E.: Neural networks, principal components, and subspaces. Int. Journal of Neural Systems 1, 61–68 (1989)

    Article  MathSciNet  Google Scholar 

  38. Oja, E.: PCA, ICA, and nonlinear Hebbian learning. In: Proc. Int. Conf. on Artificial Neural Networks (ICANN 1995), pp. 89–94(1995)

    Google Scholar 

  39. Pajunen, P., Karhunen, J.: A maximum likelihood approach to nonlinear blind source separation. In: Proc. Int. Conf. on Artificial Neural Networks (ICANN 1997), pp. 541–546 (1997)

    Google Scholar 

  40. Pajunen, P., Hyvärinen, A., Karhunen, J.: Nonlinear blind source separation by self organising maps. In: Proc. ICONIP 1996, pp. 1207–1210 (1996)

    Google Scholar 

  41. Ripley, B.D.: Pattern Recognition and Neural Networks. Cambridge University Press, Cambridge (1996)

    MATH  Google Scholar 

  42. Ritter, H., Martinetz, T., Schulten, K.: Neural Computation and Self-organising Maps: An Introduction. Addison-Wesley Publishing Company, Reading (1992)

    Google Scholar 

  43. Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323–2326 (2000)

    Article  Google Scholar 

  44. Sanger, T.D.: Optimal unsupervised learning in a single-layer linear feedforward network. Neural Networks 2, 459–473 (1991)

    Article  Google Scholar 

  45. Sammon, J.W.: A nonlinear mapping for data structure analysis. IEEE Trans. on Computer 18, 401–409 (1969)

    Article  Google Scholar 

  46. Schölkopf, B., Smola, A., Müller, K.R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation 10, 1299–1319 (1998)

    Article  Google Scholar 

  47. Taleb, A., Jutten, C.: Source separation in postnonlinear mixtures. IEEE Trans. On Signal Processing 47, 2807–2820 (1999)

    Article  Google Scholar 

  48. Tan, Y., Wang, J., Zurada, J.M.: Nonlinear blind source separation using a radial basis function network. IEEE Trans. on Neural Networks 12, 124–134 (2001)

    Article  Google Scholar 

  49. Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)

    Article  Google Scholar 

  50. Tibshirani, R.: Principal curves revisited. Statistics and Computation 2, 183–190 (1992)

    Article  Google Scholar 

  51. Törönen, P., Kolehmainen, K., Wong, G., Castrén, E.: Analysis of gene expression data using self-organising maps. FEBS Letters 451, 142–146 (1999)

    Article  Google Scholar 

  52. Ultsch, A.: Self-organising neural networks for visualisation and classification. In: Opitz, O., Lausen, B., Klar, R. (eds.) Information and Classification, pp. 864–867 (1993)

    Google Scholar 

  53. Xu, L., Cheung, C.C., Amari, S.-I.: Learned parametric mixture based ICA algorithm. Neurocomputing 22, 69–80 (1998)

    Article  MATH  Google Scholar 

  54. Yin, H.: Visualisation induced SOM (ViSOM). In: Allinson, N., Yin, H., Allinson, L., Slack, J. (eds.) Advances in Self-Organising Maps (Proc. WSOM 2001), pp. 81–88. Springer, Heidelberg (2001)

    Google Scholar 

  55. Yin, H.: ViSOM-A novel method for multivariate data projection and structure visualisation. IEEE Trans. on Neural Networks 13, 237–243 (2002)

    Article  Google Scholar 

  56. Yin, H.: Data visualisation and manifold mapping using the ViSOM. Neural Networks 15, 1005–1016 (2002)

    Article  Google Scholar 

  57. Yin, H., Allinson, N.M.: Interpolating self-organising map (iSOM). Electronics Letters 35, 1649–1650 (1999)

    Article  Google Scholar 

  58. Yin, H., Allinson, N.M.: Bayesian self-organising map for Gaussian mixtures. In: IEE Proc. –Vis. Image Signal Processing, vol. 148, pp. 234–240 (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Electrical Engineering and Electronics, University of Manchester Institute of Science and Technology, Manchester, M60 1QD, UK

    Hujun Yin

Authors
  1. Hujun Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Jiming Liu

  2. Department of Computer Science, Hong Kong Baptist University, Hong Kong

    Yiu-ming Cheung

  3. School of Electrical and Electronic Engineering, University of Manchester, UK

    Hujun Yin

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yin, H. (2003). Nonlinear Multidimensional Data Projection and Visualisation. In: Liu, J., Cheung, Ym., Yin, H. (eds) Intelligent Data Engineering and Automated Learning. IDEAL 2003. Lecture Notes in Computer Science, vol 2690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45080-1_49

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-45080-1_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40550-4

  • Online ISBN: 978-3-540-45080-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation