Package org.drip.learning.kernel

Class SymmetricRdToNormedR1Kernel

java.lang.Object
org.drip.learning.kernel.SymmetricRdToNormedR1Kernel
Direct Known Subclasses:
MercerKernel
public abstract class SymmetricRdToNormedR1Kernel
extends java.lang.Object
SymmetricRdToNormedR1Kernel exposes the Functionality behind the Kernel that is Normed Rd X Normed Rd To Supremum R1, that is, a Kernel that symmetric in the Input Metric Vector Space in terms of both the Metric and the Dimensionality.

The References are:

  • Ash, R. (1965): Information Theory Inter-science New York
  • Konig, H. (1986): Eigenvalue Distribution of Compact Operators Birkhauser Basel, Switzerland
  • Smola, A. J., A. Elisseff, B. Scholkopf, and R. C. Williamson (2000): Entropy Numbers for Convex Combinations and mlps, in: Advances in Large Margin Classifiers, A. Smola, P. Bartlett, B. Scholkopf, and D. Schuurmans - editors MIT Press Cambridge, MA


Author:
Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    SymmetricRdToNormedR1Kernel​(RdNormed rdContinuousInput, R1Normed r1ContinuousOutput)
    SymmetricRdToNormedR1Kernel Constructor

  • Method Summary

    Modifier and Type Method Description
    abstract double evaluate​(double[] adblX, double[] adblY)
    Compute the Kernel's R^d X R^d To R^1 Value
    int featureSpaceDimension()
    Compute the Feature Space Input Dimension
    RdNormed inputMetricVectorSpace()
    Retrieve the Symmetric Input Metric R^d Vector Space
    R1Normed outputMetricVectorSpace()
    Retrieve the Output R^1 Metric Vector Space

    Methods inherited from class java.lang.Object

    equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • SymmetricRdToNormedR1Kernel

      public SymmetricRdToNormedR1Kernel​(RdNormed rdContinuousInput, R1Normed r1ContinuousOutput) throws java.lang.Exception
      SymmetricRdToNormedR1Kernel Constructor
      Parameters:
      rdContinuousInput - The Symmetric Input R^d Metric Vector Space
      r1ContinuousOutput - The Output R^1 Metric Vector Space
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • inputMetricVectorSpace

      public RdNormed inputMetricVectorSpace()
      Retrieve the Symmetric Input Metric R^d Vector Space
      Returns:
      The Symmetric Input Metric R^d Vector Space

    • outputMetricVectorSpace

      public R1Normed outputMetricVectorSpace()
      Retrieve the Output R^1 Metric Vector Space
      Returns:
      The Output R^1 Metric Vector Space

    • featureSpaceDimension

      public int featureSpaceDimension()
      Compute the Feature Space Input Dimension
      Returns:
      The Feature Space Input Dimension

    • evaluate

      public abstract double evaluate​(double[] adblX, double[] adblY) throws java.lang.Exception
      Compute the Kernel's R^d X R^d To R^1 Value
      Parameters:
      adblX - Validated Vector Instance X
      adblY - Validated Vector Instance Y
      Returns:
      The Kernel's R^d X R^d To R^1 Value
      Throws:
      java.lang.Exception - Thrown if the Inputs are invalid