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Transactions on Computational Science I pp 61–84Cite as

Topology Representing Network Map – A New Tool for Visualization of High-Dimensional Data

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Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 4750))

Abstract

In practical data mining problems high-dimensional data has to be analyzed. In most of these cases it is very informative to map and visualize the hidden structure of complex data set in a low-dimensional space. The aim of this paper is to propose a new mapping algorithm based both on the topology and the metric of the data.

The utilized Topology Representing Network (TRN) combines neural gas vector quantization and competitive Hebbian learning rule in such a way that the hidden data structure is approximated by a compact graph representation. TRN is able to define a low-dimensional manifold in the high-dimensional feature space. In case the existence of a manifold, multidimensional scaling and/or Sammon mapping of the graph distances can be used to form the map of the TRN (TRNMap).

The systematic analysis of the algorithms that can be used for data visualization and the numerical examples presented in this paper demonstrate that the resulting map gives a good representation of the topology and the metric of complex data sets, and the component plane representation of TRNMap is useful to explore the hidden relations among the features.

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Authors and Affiliations

  1. Department of Mathematics and Computing, University of Pannonia, P.O. Box 158, Veszprem, H-8201, Hungary

    Agnes Vathy-Fogarassy

  2. Department of Information Systems, Eötvös Lóránd University, P.O. Box 120, H-1518, Budapest, Hungary

    Attila Kiss

  3. Department of Process Engineering, University of Pannonia, P.O. Box 158, Veszprem, H-8201, Hungary

    Janos Abonyi

Authors
  1. Agnes Vathy-Fogarassy
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  2. Attila Kiss
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  3. Janos Abonyi
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Marina L. Gavrilova C. J. Kenneth Tan

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© 2008 Springer-Verlag Berlin Heidelberg

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Vathy-Fogarassy, A., Kiss, A., Abonyi, J. (2008). Topology Representing Network Map – A New Tool for Visualization of High-Dimensional Data. In: Gavrilova, M.L., Tan, C.J.K. (eds) Transactions on Computational Science I. Lecture Notes in Computer Science, vol 4750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79299-4_3

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  • DOI: https://doi.org/10.1007/978-3-540-79299-4_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-79298-7

  • Online ISBN: 978-3-540-79299-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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