Class PolynomialKernel

java.lang.Object

smile.math.kernel.Polynomial

smile.math.kernel.PolynomialKernel

All Implemented Interfaces:

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

public class PolynomialKernel
extends Polynomial
implements MercerKernel<double[]>

The polynomial kernel.

k(u, v) = (γ u^Tv - λ)^d

where γ is the scale of the used inner product, λ the offset of the used inner product, and d the order of the polynomial kernel.

See Also:

• Serialized Form

Field Summary

Fields inherited from interface Function

logger

Constructor Summary

Constructors

Constructor	Description
PolynomialKernel(int degree)	Constructor with scale 1 and offset 0.
PolynomialKernel(int degree, double scale, double offset)	Constructor.
PolynomialKernel(int degree, double scale, double offset, 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).
PolynomialKernel	of(double[] params)	Returns the same kind kernel with the new hyperparameters.

Methods inherited from class Polynomial

degree, k, kg, offset, scale, toString

Methods inherited from class Object

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

Methods inherited from interface DotProductKernel

apply, f, K

Methods inherited from interface Function

inv, root

Methods inherited from interface MercerKernel

apply, applyAsDouble, K, K, KG

Constructor Details

PolynomialKernel

public PolynomialKernel(int degree)

Constructor with scale 1 and offset 0.

Parameters:

degree - The degree of polynomial.

PolynomialKernel

public PolynomialKernel(int degree,
 double scale,
 double offset)

Constructor.

Parameters:

degree - The degree of polynomial.

scale - The scale parameter.

offset - The offset parameter.

PolynomialKernel

public PolynomialKernel(int degree,
 double scale,
 double offset,
 double[] lo,
 double[] hi)

Constructor.

Parameters:

degree - The degree of polynomial. The degree is fixed during hyperparameter tuning.

scale - The scale parameter.

offset - The offset parameter.

lo - The lower bound of scale and offset for hyperparameter tuning.

hi - The upper bound of scale and offset 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 PolynomialKernel 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.