Package smile.math.kernel

Class HyperbolicTangent

java.lang.Object
smile.math.kernel.HyperbolicTangent
All Implemented Interfaces:
Serializable, Function, DotProductKernel
Direct Known Subclasses:
BinarySparseHyperbolicTangentKernel, HyperbolicTangentKernel, SparseHyperbolicTangentKernel
public class HyperbolicTangent extends 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:

  • 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 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

  • 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.