smile.math.kernel

Class PolynomialKernel

java.lang.Object

smile.math.kernel.Polynomial

smile.math.kernel.PolynomialKernel

All Implemented Interfaces:

java.io.Serializable, java.util.function.ToDoubleBiFunction<double[],double[]>, Function, DotProductKernel, MercerKernel<double[]>

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

The polynomial kernel.

     k(u, v) = (γ uTv - 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

Constructor Summary

Constructors

Constructor and 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 and Description
double[]	hi() Returns the upper bound of hyperparameters.
double[]	hyperparameters() Returns the hyperparameters for tuning.
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.
PolynomialKernel	of(double[] params) Returns the same kind kernel with the new hyperparameters.

Methods inherited from class smile.math.kernel.Polynomial

degree, k, kg, offset, 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.kernel.MercerKernel

apply, applyAsDouble, K, K, KG

Methods inherited from interface smile.math.kernel.DotProductKernel

apply, f, K

Constructor Detail

PolynomialKernel

public PolynomialKernel(int degree)

Constructor with scale 1 and offset 0.

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 Detail

k

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

Description copied from interface: MercerKernel

Kernel function.

Specified by:

k in interface MercerKernel<double[]>

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[]>

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[]>

hyperparameters

public double[] hyperparameters()

Description copied from interface: MercerKernel

Returns the hyperparameters for tuning.

Specified by:

hyperparameters in interface MercerKernel<double[]>

lo

public double[] lo()

Description copied from interface: MercerKernel

Returns the lower bound of hyperparameters.

Specified by:

lo in interface MercerKernel<double[]>

hi

public double[] hi()

Description copied from interface: MercerKernel

Returns the upper bound of hyperparameters.

Specified by:

hi in interface MercerKernel<double[]>