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GEOSTATS: radial basis functions

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  • Nicola Fohrer
    Dear colleagues, does anybody have experience in using radial basis functions for the interpolation of small data sets. Where are the limits of this methods?
    Message 1 of 2 , Dec 8, 1997
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      Dear colleagues,

      does anybody have experience in using radial basis functions for the
      interpolation of small data sets. Where are the limits of this
      methods? Which literature would you recommend?

      thank you in advance
      Nicola Fohrer



      ********************************
      Dr. sc. agr. Nicola Fohrer
      Wissenschaftliche Assistentin
      Institut fuer Landeskultur
      Senckenbergstr. 3
      35 390 Giessen
      Tel:0641/99 37385
      Fax:0641/99 37389
      email:Nicola.Fohrer@...-giessen.de

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    • Syed Abdul Rahman
      ... See my recent paper presented at the recent IAMG in Barcelona (Review of AI-Based Interpolators for Spatial Mapping). Included are RBF networks (radial
      Message 2 of 2 , Dec 9, 1997
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        > From: Nicola Fohrer <Nicola.Fohrer@...-giessen.de>
        > does anybody have experience in using radial basis functions for the
        > interpolation of small data sets. Where are the limits of this
        > methods? Which literature would you recommend?

        See my recent paper presented at the recent IAMG in Barcelona
        (Review of AI-Based Interpolators for Spatial Mapping). Included
        are RBF networks (radial basis functions viewed from an AI
        perspective), a fuzzy logic interpolator, and conventional
        back propagation neural networks (co-authors Maignan and Wong).

        In addition to Dr. Myer's comments:

        a. We have had several attempts at using RBFs in "cross-validation"
        mode, to derive the best RBF width (or "range") for a set of raw
        data, before doing interpolation. This can be automated via the
        computer. This is also applicable to fuzzy logic interpolation,
        optimizing on a particular fuzzy function for "distance" between
        points. One can presumably go a step farther by optimizing on
        the control constant for _each_ data in the search neighborhood
        (i.e. a local spatial correlation correlation measure). I have read
        somewhere (I think it was P. Kitanidis's textbook) that hydrogeologists
        have used this sort of approach albeit via the variogram measure.

        b. RBFs are quite amenable for the incorporation of diverse sources
        of data, avoiding conventional cross-variogram or cross-correlation
        modeling under (in most cases) strict positive definite conditions,
        with "acceptable" results (e.g. compared to co-kriging). We don't actually
        model the data-to-data covariances, just the data-to-location
        covariances for each variate in the input neuron. Depending on your
        data configuration and quality, this might not always work.

        c. We've had mixed views on the general use of AI-based interpolators.
        We've had success using them to remove trend components,
        and for exact interpolation (via Interpolation neural nets), but
        difficulties
        have arisen in trying to derive an error measure for cases where
        back propagation was used. We like the ease with which multivariate
        data can be incorporated, and I think this is a strength.

        Regards,

        Syed

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