Package smile.math.kernel

Class ThinPlateSplineKernel

java.lang.Object

smile.math.kernel.ThinPlateSpline

smile.math.kernel.ThinPlateSplineKernel

All Implemented Interfaces:

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

public class ThinPlateSplineKernel
extends ThinPlateSpline
implements MercerKernel<double[]>

The Thin Plate Spline kernel.

k(u, v) = (||u-v|| / σ)² log (||u-v|| / σ)

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

See Also:

• Serialized Form

Constructor Summary

Constructors

Constructor	Description
ThinPlateSplineKernel(double sigma)	Constructor.
ThinPlateSplineKernel(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).
ThinPlateSplineKernel	of(double[] params)	Returns the same kind kernel with the new hyperparameters.

Methods inherited from class smile.math.kernel.ThinPlateSpline

k, kg, scale, toString

Methods inherited from class java.lang.Object

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

Methods inherited from interface smile.math.Function

inv

Methods inherited from interface smile.math.kernel.IsotropicKernel

apply, f, K, KG

Methods inherited from interface smile.math.kernel.MercerKernel

apply, applyAsDouble, K, K, KG

Constructor Details

ThinPlateSplineKernel

public ThinPlateSplineKernel(double sigma)

Constructor.

Parameters:

sigma - The length scale of kernel.

ThinPlateSplineKernel

public ThinPlateSplineKernel(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 ThinPlateSplineKernel 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.