Package smile.math.rbf

Class GaussianRadialBasis

java.lang.Object
smile.math.rbf.GaussianRadialBasis
All Implemented Interfaces:
Serializable, Function, RadialBasisFunction
public class GaussianRadialBasis extends Object implements RadialBasisFunction
Gaussian RBF. φ(r) = exp(-0.5 * r2 / r02) 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

  1. Nabil Benoudjit and Michel Verleysen. On the kernel widths in radial-basis function networks. Neural Process, 2003.
See Also:

  • Constructor Details

    • GaussianRadialBasis

      public GaussianRadialBasis()
      Constructor. The default scale is 1.0.

    • GaussianRadialBasis

      public GaussianRadialBasis(double scale)
      Constructor.
      Parameters:
      scale - the scale parameter.

  • Method Details

    • f

      public double f(double r)
      Description copied from interface: Function
      Computes the value of the function at x.
      Specified by:
      f in interface Function
      Parameters:
      r - a real number.
      Returns:
      the function value.

    • toString

      public String toString()
      Overrides:
      toString in class Object