smile.math.kernel

Class HyperbolicTangent

java.lang.Object

smile.math.kernel.HyperbolicTangent

All Implemented Interfaces:

java.io.Serializable, Function, DotProductKernel

Direct Known Subclasses:

BinarySparseHyperbolicTangentKernel, HyperbolicTangentKernel, SparseHyperbolicTangentKernel

public class HyperbolicTangent
extends java.lang.Object
implements DotProductKernel

The hyperbolic tangent kernel.

     k(u, v) = tanh(γ uTv - 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

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and 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.
java.lang.String	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

Constructor Detail

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 Detail

scale

public double scale()

Returns the scale of kernel.

offset

public double offset()

Returns the offset of kernel.

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.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.

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.