Data visualisation and manifold mapping using the ViSOM

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    Abstract

    The self-organising map (SOM) has been successfully employed as a nonparametric method for dimensionality reduction and data visualisation. However, for visualisation the SOM requires a colouring scheme to imprint the distances between neurons so that the clustering and boundaries can be seen. Even though the distributions of the data and structures of the clusters are not faithfully portrayed on the map. Recently an extended SOM, called the visualisation-induced SOM (ViSOM) has been proposed to directly preserve the distance information on the map, along with the topology. The ViSOM constrains the lateral contraction forces between neurons and hence regularises the inter-neuron distances so that distances between neurons in the data space are in proportion to those in the map space. This paper shows that it produces a smooth and graded mesh in the data space and captures the nonlinear manifold of the data. The relationships between the ViSOM and the principal curve/surface are analysed. The ViSOM represents a discrete principal curve or surface and is a natural algorithm for obtaining principal curves/surfaces. Guidelines for applying the ViSOM constraint and setting the resolution parameter are also provided, together with experimental results and comparisons with the SOM, Sammon mapping and principal curve methods. © 2002 Elsevier Science Ltd. All rights reserved.
    Original languageEnglish
    Pages (from-to)1005-1016
    Number of pages11
    JournalNeural Networks
    Volume15
    Issue number8-9
    DOIs
    Publication statusPublished - Oct 2002

    Keywords

    • Dimensionality reduction
    • Multidimensional scaling
    • Multivariate data visualisation
    • Principal curves and surfaces
    • Self-organising maps

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