Class Gaussian

java.lang.Object

smile.math.kernel.Gaussian

All Implemented Interfaces:

Serializable, IsotropicKernel, Function

Direct Known Subclasses:

BinarySparseGaussianKernel, GaussianKernel, SparseGaussianKernel

public class Gaussian
extends Object
implements IsotropicKernel

Gaussian kernel, also referred as RBF kernel or squared exponential kernel.

k(u, v) = exp(-||u-v||² / 2σ²)

where σ > 0 is the scale parameter of the kernel.

The Gaussian kernel is a good choice for a great deal of applications, although sometimes it is remarked as being overused.

See Also:

• Serialized Form

Field Summary

Fields inherited from interface Function

logger

Constructor Summary

Constructors

Constructor	Description
Gaussian(double sigma, double lo, double hi)	Constructor.

Method Summary

Modifier and Type	Method	Description
double	k(double dist)	Computes the isotropic kernel function.
double[]	kg(double dist)	Computes the isotropic kernel function and its gradient over hyperparameters.
double	scale()	Returns the length scale of kernel.
String	toString()

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface Function

inv, root

Methods inherited from interface IsotropicKernel

apply, f, K, KG

Constructor Details

Gaussian

public Gaussian(double sigma,
 double lo,
 double hi)

Constructor.

Parameters:

sigma - The length scale of kernel.

lo - The lower bound of length scale for hyperparameter tuning.

hi - The upper bound of length scale for hyperparameter tuning.

Method Details

scale

public double scale()

Returns the length scale of kernel.

Returns:

the length scale of kernel.

toString

public String toString()

Overrides:

toString in class Object

k

public double k(double dist)

Description copied from interface: IsotropicKernel

Computes the isotropic kernel function.

Specified by:

k in interface IsotropicKernel

Parameters:

dist - The distance.

Returns:

the kernel value.

kg

public double[] kg(double dist)

Description copied from interface: IsotropicKernel

Computes the isotropic kernel function and its gradient over hyperparameters.

Specified by:

kg in interface IsotropicKernel

Parameters:

dist - The distance.

Returns:

the kernel value and gradient.