smile.math.rbf

Class GaussianRadialBasis

java.lang.Object

smile.math.rbf.GaussianRadialBasis

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

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

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and Description
GaussianRadialBasis() Constructor.
GaussianRadialBasis(double scale) Constructor.

Method Summary

Modifier and Type	Method and Description
double	f(double r) Compute the value of the function at x.
java.lang.String	toString()

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

GaussianRadialBasis

public GaussianRadialBasis()

Constructor. The default bandwidth is 1.0.

GaussianRadialBasis

public GaussianRadialBasis(double scale)

Constructor.

Parameters:

scale - the scale (bandwidth/sigma) parameter.

Method Detail

f

public double f(double r)

Description copied from interface: Function

Compute the value of the function at x.

Specified by:

f in interface Function

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object