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Data visualisation and manifold mapping using the ViSOM.

Hujun Yin1

  • 1Department of Electrical Engineering and Electronics, UMIST, Manchester, UK. h.yin@umist.ac.uk

Neural Networks : the Official Journal of the International Neural Network Society
|November 6, 2002
PubMed
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The visualization-induced SOM (ViSOM) improves data visualization by preserving topological and distance information. This method enhances cluster boundary representation and captures nonlinear data manifolds more effectively than traditional SOMs.

Area of Science:

  • Data Science
  • Machine Learning
  • Computational Statistics

Background:

  • Self-organizing maps (SOMs) are established for dimensionality reduction and visualization.
  • Traditional SOMs struggle to faithfully represent data distributions and cluster structures due to indirect distance portrayal.
  • Existing methods require coloring schemes to infer distances, often distorting data topology.

Purpose of the Study:

  • Introduce the visualization-induced SOM (ViSOM) to directly preserve distance and topological information.
  • Enhance the accuracy of data visualization and cluster boundary representation.
  • Analyze the relationship between ViSOM and principal curves/surfaces.

Main Methods:

  • The ViSOM employs constrained lateral contraction forces between neurons.

Related Experiment Videos

  • This regularization ensures inter-neuron distances in map space are proportional to data space distances.
  • The method generates a smooth mesh, capturing nonlinear data manifolds.

    • Main Results:

    • ViSOM produces a smooth, graded mesh that accurately reflects data space structure.
    • It effectively captures nonlinear manifolds present in the data.
    • ViSOM is shown to be a discrete representation of principal curves/surfaces.

    Conclusions:

    • ViSOM offers superior visualization by preserving intrinsic data geometry and topology.
    • It provides a natural algorithmic approach for obtaining principal curves/surfaces.
    • The study offers practical guidelines for ViSOM application and parameter tuning.