Class GaussianKernel

java.lang.Object

smile.math.kernel.Gaussian

smile.math.kernel.GaussianKernel

All Implemented Interfaces:

Serializable, ToDoubleBiFunction<double[],double[]>, IsotropicKernel, MercerKernel<double[]>, Function

public class GaussianKernel
extends Gaussian
implements MercerKernel<double[]>

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
GaussianKernel(double sigma)	Constructor.
GaussianKernel(double sigma, double lo, double hi)	Constructor.

Method Summary

Modifier and Type	Method	Description
double[]	hi()	Returns the upper bound of hyperparameters (in hyperparameter tuning).
double[]	hyperparameters()	Returns the hyperparameters of kernel.
double	k(double[] x, double[] y)	Kernel function.
double[]	kg(double[] x, double[] y)	Computes the kernel and its gradient over hyperparameters.
double[]	lo()	Returns the lower bound of hyperparameters (in hyperparameter tuning).
GaussianKernel	of(double[] params)	Returns the same kind kernel with the new hyperparameters.

Methods inherited from class Gaussian

k, kg, scale, 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

Methods inherited from interface MercerKernel

apply, applyAsDouble, K, K, KG

Constructor Details

GaussianKernel

public GaussianKernel(double sigma)

Constructor.

Parameters:

sigma - The length scale of kernel.

GaussianKernel

public GaussianKernel(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

k

public double k(double[] x,
 double[] y)

Description copied from interface: MercerKernel

Kernel function.

Specified by:

k in interface MercerKernel<double[]>

Parameters:

x - an object.

y - an object.

Returns:

the kernel value.

kg

public double[] kg(double[] x,
 double[] y)

Description copied from interface: MercerKernel

Computes the kernel and its gradient over hyperparameters.

Specified by:

kg in interface MercerKernel<double[]>

Parameters:

x - an object.

y - an object.

Returns:

the kernel value and gradient.

of

public GaussianKernel of(double[] params)

Description copied from interface: MercerKernel

Returns the same kind kernel with the new hyperparameters.

Specified by:

of in interface MercerKernel<double[]>

Parameters:

params - the hyperparameters.

Returns:

the same kind kernel with the new hyperparameters.

hyperparameters

public double[] hyperparameters()

Description copied from interface: MercerKernel

Returns the hyperparameters of kernel.

Specified by:

hyperparameters in interface MercerKernel<double[]>

Returns:

the hyperparameters of kernel.

lo

public double[] lo()

Description copied from interface: MercerKernel

Returns the lower bound of hyperparameters (in hyperparameter tuning).

Specified by:

lo in interface MercerKernel<double[]>

Returns:

the lower bound of hyperparameters.

hi

public double[] hi()

Description copied from interface: MercerKernel

Returns the upper bound of hyperparameters (in hyperparameter tuning).

Specified by:

hi in interface MercerKernel<double[]>

Returns:

the upper bound of hyperparameters.