smile.math.kernel

Class Gaussian

java.lang.Object

smile.math.kernel.Gaussian

All Implemented Interfaces:

java.io.Serializable, Function, IsotropicKernel

Direct Known Subclasses:

BinarySparseGaussianKernel, GaussianKernel, SparseGaussianKernel

public class Gaussian
extends java.lang.Object
implements IsotropicKernel

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

     k(u, v) = e-||u-v||2 / (2 * σ2)
 

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

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and 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.
java.lang.String	toString()

Methods inherited from class java.lang.Object

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

Methods inherited from interface smile.math.kernel.IsotropicKernel

apply, f, K, KG

Constructor Detail

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 Detail

scale

public double scale()

Returns the length scale of kernel.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.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.

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.