Package org.drip.learning.kernel

Class MercerKernel

java.lang.Object

org.drip.learning.kernel.SymmetricRdToNormedR1Kernel

org.drip.learning.kernel.MercerKernel

public class MercerKernel
extends SymmetricRdToNormedR1Kernel

MercerKernel exposes the Functionality behind the Eigenized Kernel that is Normed R^x X Normed R^x To Supremum R¹

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

• Module = Computational Core Module
• Library = Statistical Learning
• Project = Agnostic Learning Bounds under Empirical Loss Minimization Schemes
• Package = Statistical Learning Banach Mercer Kernels

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
MercerKernel(IntegralOperatorEigenContainer ioec)	MercerKernel Constructor

Method Summary

Modifier and Type	Method	Description
IntegralOperatorEigenContainer	eigenComponentSuite()	Retrieve the Suite of Eigen Components
double	evaluate(double[] adblX, double[] adblY)	Compute the Kernel's R^d X R^d To R^1 Value

Methods inherited from class org.drip.learning.kernel.SymmetricRdToNormedR1Kernel

featureSpaceDimension, inputMetricVectorSpace, outputMetricVectorSpace

Methods inherited from class java.lang.Object

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

Constructor Details

MercerKernel

public MercerKernel(IntegralOperatorEigenContainer ioec)
             throws java.lang.Exception

MercerKernel Constructor

Parameters:

ioec - The Container of the Eigen Components

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

eigenComponentSuite

public IntegralOperatorEigenContainer eigenComponentSuite()

Retrieve the Suite of Eigen Components

Returns:

The Suite of Eigen Components

evaluate

public double evaluate(double[] adblX,
double[] adblY)
                throws java.lang.Exception

Description copied from class: SymmetricRdToNormedR1Kernel

Compute the Kernel's R^d X R^d To R^1 Value

Specified by:

evaluate in class SymmetricRdToNormedR1Kernel

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