Package org.drip.learning.kernel

Class IntegralOperatorEigenComponent

java.lang.Object
org.drip.learning.kernel.IntegralOperatorEigenComponent
public class IntegralOperatorEigenComponent
extends java.lang.Object
IntegralOperatorEigenComponent holds the Eigen-Function Space and the Eigenvalue Functions/Spaces of the Rx L2 To Rx L2 Kernel Linear Integral Operator defined by: T_k [f(.)] := Integral Over Input Space {k (., y) * f(y) * d[Prob(y)]}

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
    IntegralOperatorEigenComponent​(EigenFunctionRdToR1 efRdToR1, double dblEigenValue)
    IntegralOperatorEigenComponent Constructor

  • Method Summary

    Modifier and Type Method Description
    EigenFunctionRdToR1 eigenFunction()
    Retrieve the Eigen-Function
    double eigenvalue()
    Retrieve the Eigenvalue
    double evaluate​(double[] adblX, double[] adblY)
    Compute the Eigen-Component Contribution to the Kernel Value
    NormedRdToNormedR1 rkhsFeatureMap()
    Retrieve the Feature Map Space represented via the Reproducing Kernel Hilbert Space
    double rkhsFeatureParallelepipedLength()
    Retrieve the RKHS Feature Map Parallelepiped Agnostic Upper Bound Length

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • IntegralOperatorEigenComponent

      public IntegralOperatorEigenComponent​(EigenFunctionRdToR1 efRdToR1, double dblEigenValue) throws java.lang.Exception
      IntegralOperatorEigenComponent Constructor
      Parameters:
      efRdToR1 - Normed R^d To Normed R^1 Eigen-Function
      dblEigenValue - The Eigenvalue
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • eigenFunction

      public EigenFunctionRdToR1 eigenFunction()
      Retrieve the Eigen-Function
      Returns:
      The Eigen-Function

    • eigenvalue

      public double eigenvalue()
      Retrieve the Eigenvalue
      Returns:
      The Eigenvalue

    • rkhsFeatureMap

      public NormedRdToNormedR1 rkhsFeatureMap()
      Retrieve the Feature Map Space represented via the Reproducing Kernel Hilbert Space
      Returns:
      The Feature Map Space representation using the Reproducing Kernel Hilbert Space

    • rkhsFeatureParallelepipedLength

      public double rkhsFeatureParallelepipedLength()
      Retrieve the RKHS Feature Map Parallelepiped Agnostic Upper Bound Length
      Returns:
      The RKHS Feature Map Parallelepiped Agnostic Upper Bound Length

    • evaluate

      public double evaluate​(double[] adblX, double[] adblY) throws java.lang.Exception
      Compute the Eigen-Component Contribution to the Kernel Value
      Parameters:
      adblX - The X Variate Array
      adblY - The Y Variate Array
      Returns:
      The Eigen-Component Contribution to the Kernel Value
      Throws:
      java.lang.Exception - Thrown if the Inputs are invalid