Visualisation Induced SOM (ViSOM)

  • Hujun Yin
Conference paper

Abstract

When used for visualisation of high dimensional data, the self-organising map (SOM) requires a colouring scheme such as U-matrix to mark the distances between neurons. Even so, the structures of the data clusters may not be apparent and their shapes are often distorted. In this paper, a visualisation-induced SOM (ViSOM) is proposed as a new tool for data visualisation. The algorithm constrains the lateral contraction forces between a winning neuron and its neighbouring ones and hence regularises the inter-neuron distances. The mapping preserves directly the interneuron distances on the map along with the topology. It produces a graded mesh in the data space and can accommodate both training data and new arrivals. The ViSOM represents a class of discrete principal curves and surfaces.

Keywords

Entropy Covariance Hexagonal Sammon 

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References

  1. [1].
    Sammon, J.W., “A nonlinear mapping for data structure analysis,” IEEE Trans on Computer, vol. C-18(5), pp. 401-409, 1969.CrossRefGoogle Scholar
  2. [2].
    Mao, J. and Jain, A.K., “Artificial Neural Networks for Feature Extraction and Multivariate Data Projection,” IEEE Trans. on Neural Networks, vol. 6, pp. 296-317, 1995.CrossRefGoogle Scholar
  3. [3].
    Kohonen, T., Self-Organising Maps, Springer: Berlin, 1995.Google Scholar
  4. [4].
    Ultsch, A., “Self-organising neural networks for visualisation and classification,” in Information and Classification, O. Opitz, B. Lausen and R. Klar eds., pp. 864-867, 1993Google Scholar
  5. [5].
    Kraaijveld, M.A., Mao, J. and Jain, A.K., “A nonlinear projection method based on Kohonen’s topology preserving maps,” IEEE Trans. Neural Networks, vol. 6, pp. 548-559, 1995.CrossRefGoogle Scholar
  6. [6].
    Yin, H. and Allinson, N.M., “Interpolating self-organisng map (iSOM),” Electronics Letters, vol. 35, pp. 1649-1650, 1999.CrossRefGoogle Scholar
  7. [7].
    Hastie, T. and Stuetzle, W., “Principal curves,” Journal of the American Statistical Association, vol. 84, pp. 502-516, 1989.MathSciNetMATHCrossRefGoogle Scholar
  8. [8].
    Malthouse, E.C., “Limitations of nonlinear PCA as performed with generic neural networks,” IEEE Trans. Neural Networks, vol. 9, pp. 165-173, 1998.CrossRefGoogle Scholar
  9. [9].
    Ripley, B.D., Pattern Recognition and Neural Networks, Cambridge University Press: Cambridge, UK, 1996.MATHGoogle Scholar
  10. [10].
    Cox, T.F. and Cox, M.A.A., Multidimensional Scaling, Chapman & Hall: London, 1994.MATHGoogle Scholar
  11. [11].
    Yin, H. and Allinson, N.M., “On the distribution and convergence of feature space in self-organising maps,” Neural Computation, vol. 7, pp. 1178-1187, 1995.CrossRefGoogle Scholar
  12. [12].
    Fisher, R.A., “The use of multiple measurements in taxonomic problems,” Annual Eugenics, vol. 7, pp. 178-188, 1936.Google Scholar

Copyright information

© Springer-Verlag London Limited 2001

Authors and Affiliations

  • Hujun Yin
    • 1
  1. 1.Dept. of Electrical Engineering and ElectronicsUMISTManchesterUK

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