Package smile.math.rbf
Class GaussianRadialBasis
- java.lang.Object
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- smile.math.rbf.GaussianRadialBasis
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- All Implemented Interfaces:
java.io.Serializable
,Function
,RadialBasisFunction
public class GaussianRadialBasis extends java.lang.Object implements RadialBasisFunction, java.io.Serializable
Gaussian RBF. φ(r) = e-0.5 * r2 / r20 where r0 is a scale factor. The interpolation accuracy using Gaussian basis functions can be very sensitive to r0, and they are often avoided for this reason. However, for smooth functions and with an optimal r0, very high accuracy can be achieved. The Gaussian also will extrapolate any function to zero far from the data, and it gets to zero quickly.In general, r0 should be larger than the typical separation of points but smaller than the "outer scale" or feature size of the function to interplate. There can be several orders of magnitude difference between the interpolation accuracy with a good choice for r0, versus a poor choice, so it is definitely worth some experimentation. One way to experiment is to construct an RBF interpolator omitting one data point at a time and measuring the interpolation error at the omitted point.
References
- Nabil Benoudjit and Michel Verleysen. On the kernel widths in radial-basis function networks. Neural Process, 2003.
- Author:
- Haifeng Li
- See Also:
- Serialized Form
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Constructor Summary
Constructors Constructor Description GaussianRadialBasis()
Constructor.GaussianRadialBasis(double scale)
Constructor.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description double
f(double r)
Compute the value of the function at x.java.lang.String
toString()
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