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 R^x L2 To R^x L2 Kernel Linear Integral Operator defined by: T_k [f(.)] := Integral Over Input Space {k (., y) * f(y) * d[Prob(y)]} The References are: 1) Ash, R. (1965): Information Theory, Inter-science New York. 2) Konig, H. (1986): Eigenvalue Distribution of Compact Operators, Birkhauser, Basel, Switzerland. 3) 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 and Description
IntegralOperatorEigenComponent(EigenFunctionRdToR1 efRdToR1, double dblEigenValue) IntegralOperatorEigenComponent Constructor

Method Summary

Modifier and Type	Method and 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 Detail

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 Detail

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