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 R^d X Normed R^d To Supremum R^1, that is, a Kernel that symmetric in the Input Metric Vector Space in terms of both the Metric and the Dimensionality. 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
SymmetricRdToNormedR1Kernel(RdNormed rdContinuousInput, R1Normed r1ContinuousOutput) SymmetricRdToNormedR1Kernel Constructor

Method Summary

Modifier and Type	Method and 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 Detail

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 Detail

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