> 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
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.
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