Class HyperbolicTangent

java.lang.Object

smile.math.kernel.HyperbolicTangent

All Implemented Interfaces:

Serializable, DotProductKernel, Function

Direct Known Subclasses:

BinarySparseHyperbolicTangentKernel, HyperbolicTangentKernel, SparseHyperbolicTangentKernel

public class HyperbolicTangent
extends Object
implements DotProductKernel

The hyperbolic tangent kernel.

k(u, v) = tanh(γ u^Tv - λ)

where γ is the scale of the used inner product and λ is the offset of the used inner product. If the offset is negative the likelihood of obtaining a kernel matrix that is not positive definite is much higher (since then even some diagonal elements may be negative), hence if this kernel has to be used, the offset should always be positive. Note, however, that this is no guarantee that the kernel will be positive.

The hyperbolic tangent kernel was quite popular for support vector machines due to its origin from neural networks. However, it should be used carefully since the kernel matrix may not be positive semi-definite. Besides, it was reported the hyperbolic tangent kernel is not better than the Gaussian kernel in general.

See Also:

• Serialized Form

Field Summary

Fields inherited from interface Function

logger

Constructor Summary

Constructors

Constructor	Description
HyperbolicTangent(double scale, double offset, double[] lo, double[] hi)	Constructor.

Method Summary

Modifier and Type	Method	Description
double	k(double dot)	Computes the dot product kernel function.
double[]	kg(double dot)	Computes the dot product kernel function and its gradient over hyperparameters.
double	offset()	Returns the offset of kernel.
double	scale()	Returns the scale of kernel.
String	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

Constructor Details

HyperbolicTangent

public HyperbolicTangent(double scale,
 double offset,
 double[] lo,
 double[] hi)

Constructor.

Parameters:

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

scale

public double scale()

Returns the scale of kernel.

Returns:

the scale of kernel.

offset

public double offset()

Returns the offset of kernel.

Returns:

the offset of kernel.

toString

public String toString()

Overrides:

toString in class Object

k

public double k(double dot)

Description copied from interface: DotProductKernel

Computes the dot product kernel function.

Specified by:

k in interface DotProductKernel

Parameters:

dot - the dot product.

Returns:

the kernel value.

kg

public double[] kg(double dot)

Description copied from interface: DotProductKernel

Computes the dot product kernel function and its gradient over hyperparameters.

Specified by:

kg in interface DotProductKernel

Parameters:

dot - The dot product.

Returns:

the kernel value and gradient.