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[?] Perform an approximation with radial basis functions?

Peter a
Posted 8 years ago

Hi!

I want to approximate some functions with basisfunctions, which can be easy Fourier-transformed. So I got the idea to approximate my function with Gaussian normal-distribution curves. This led me to the idea of approximating my function with radial basis functions (RBF), such as the Gaussian curves are.

Due to this I found the "NeuralNetworks`" Mathematica package, which seems to be exactly what I was looking for. I even found this very helpful Example. Poorly this package doesn't seem to be part of Mathematica 11 anymore. The newer built-in Version doesn't seem to include functions, which do similar work.

Because I am quite new at Mathematica I have no idea if and how I can find another way to solve my problem.

Does anybody have an idea how I can approximate my function (maybe similar to the example?) with Gaussian normal-Distribution curves?

I would be very grateful, if anyone could help me!

Thanks you very much!
POSTED BY: Peter a
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POSTED BY: Michael Rogers

Hi Peter

In answer to your query about Radial Basis Function (RBF) networks, the Classify function, see http://reference.wolfram.com/language/ref/Classify.html has the Option Method->"SupportVectorMachine" which now has a sub-method "KernelType"->"RadialBasisFunction" that allows one to construct an RBF NN, so the full form would be Classify[ training data, Method->{"SupportVectorMachine", "KernelType"->"RadialBasisFunction"}]. This is not the traditional 3 layer RBF network but an extension where the number of layers is determined by the training data and other options. See the documentation at http://reference.wolfram.com/language/ref/Classify.html and http://reference.wolfram.com/language/ref/method/SupportVectorMachine.html.

Hope this helps Michael
POSTED BY: Michael Kelly
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