Package smile.math.kernel

Class SparsePolynomialKernel

java.lang.Object

smile.math.kernel.Polynomial

smile.math.kernel.SparsePolynomialKernel

All Implemented Interfaces:

Serializable, ToDoubleBiFunction<SparseArray,SparseArray>, Function, DotProductKernel, MercerKernel<SparseArray>

public class SparsePolynomialKernel
extends Polynomial
implements MercerKernel<SparseArray>

The polynomial kernel on sparse data.

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

Constructor Summary

Constructors

Constructor	Description
SparsePolynomialKernel(int degree)	Constructor with scale 1 and offset 0.
SparsePolynomialKernel(int degree, double scale, double offset)	Constructor.
SparsePolynomialKernel(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(SparseArray x, SparseArray y)	Kernel function.
double[]	kg(SparseArray x, SparseArray y)	Computes the kernel and its gradient over hyperparameters.
double[]	lo()	Returns the lower bound of hyperparameters (in hyperparameter tuning).
SparsePolynomialKernel	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.DotProductKernel

apply, f, K

Methods inherited from interface smile.math.Function

inv

Methods inherited from interface smile.math.kernel.MercerKernel

apply, applyAsDouble, K, K, KG

Constructor Details

SparsePolynomialKernel

public SparsePolynomialKernel(int degree)

Constructor with scale 1 and offset 0.

Parameters:

degree - The degree of polynomial.

SparsePolynomialKernel

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

Constructor.

Parameters:

degree - The degree of polynomial.

scale - The scale parameter.

offset - The offset parameter.

SparsePolynomialKernel

public SparsePolynomialKernel(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(SparseArray x,
 SparseArray y)

Description copied from interface: MercerKernel

Kernel function.

Specified by:

k in interface MercerKernel<SparseArray>

Parameters:

x - an object.

y - an object.

Returns:

the kernel value.

kg

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

Description copied from interface: MercerKernel

Computes the kernel and its gradient over hyperparameters.

Specified by:

kg in interface MercerKernel<SparseArray>

Parameters:

x - an object.

y - an object.

Returns:

the kernel value and gradient.

of

public SparsePolynomialKernel of(double[] params)

Description copied from interface: MercerKernel

Returns the same kind kernel with the new hyperparameters.

Specified by:

of in interface MercerKernel<SparseArray>

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<SparseArray>

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<SparseArray>

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<SparseArray>

Returns:

the upper bound of hyperparameters.