smile.math.kernel

Class HyperbolicTangentKernel

java.lang.Object

smile.math.kernel.HyperbolicTangentKernel

All Implemented Interfaces:

java.io.Serializable, MercerKernel<double[]>

public class HyperbolicTangentKernel
extends java.lang.Object
implements MercerKernel<double[]>, java.io.Serializable

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

Constructor Summary

Constructors

Constructor and Description
HyperbolicTangentKernel() Constructor.
HyperbolicTangentKernel(double scale, double offset) Constructor.

Method Summary

Modifier and Type	Method and Description
double	k(double[] x, double[] y) Kernel function.
java.lang.String	toString()

Methods inherited from class java.lang.Object

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

Constructor Detail

HyperbolicTangentKernel

public HyperbolicTangentKernel()

Constructor.

HyperbolicTangentKernel

public HyperbolicTangentKernel(double scale,
                               double offset)

Constructor.

Method Detail

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object

k

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

Description copied from interface: MercerKernel

Kernel function.

Specified by:

k in interface MercerKernel<double[]>