org.drip.learning.svm

Class RdDecisionFunction

java.lang.Object

org.drip.function.definition.RdToR1

org.drip.learning.svm.RdDecisionFunction

Direct Known Subclasses:

KernelRdDecisionFunction, LinearRdDecisionFunction

public abstract class RdDecisionFunction
extends RdToR1

RdDecisionFunction exposes the R^d Decision-Function Based SVM Functionality for Classification and Regression. The References are: 1) Vapnik, V., and A. Chervonenkis (1974): Theory of Pattern Recognition (in Russian), Nauka, Moscow USSR. 2) Vapnik, V. (1995): The Nature of Statistical Learning, Springer-Verlag, New York. 3) Shawe-Taylor, J., P. L. Bartlett, R. C. Williamson, and M. Anthony (1996): A Framework for Structural Risk Minimization, in: Proceedings of the 9th Annual Conference on Computational Learning Theory, ACM New York 68-76.

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor and Description
RdDecisionFunction(RdGeneralizedVector rdPredictor, RdNormed rdInverseMargin, double[] adblInverseMarginWeight, double dblB) RdDecisionFunction Constructor

Method Summary

Modifier and Type	Method and Description
short	classify(double[] adblX) Classify the Specified Multi-dimensional Point
DecisionFunctionOperatorBounds	entropyNumberUpperBounds(DiagonalScalingOperator dsoFactorizer, double dblFeatureSpaceMaureyConstant) Compute the Entropy Number Upper Bounds Instance for the Specified Inputs
RdNormed	inverseMarginSpace() Retrieve the Inverse Margin Weight Metric Vector Space
double[]	inverseMarginWeights() Retrieve the Decision Kernel Weights
double	logEntropyNumberAsymptote(DiagonalScalingOperator dsoFactorizer) Compute the Decision Function's Asymptotic Exponent for the Entropy Number
double	offset() Retrieve the Offset
abstract boolean	optimizeClassificationHyperplane(short[] asEmpirical, double dblMargin, double dblInverseWidthNormConstraint) Optimize the Hyper-plane for the Purposes of Classification
abstract boolean	optimizeRegressionHyperplane(double[] adblEmpirical, double dblMargin, double dblInverseWidthNormConstraint) Optimize the Hyper-plane for the Purposes of Regression
RdGeneralizedVector	predictorSpace() Retrieve the Input Predictor Metric Vector Space
double	regress(double[] adblX) Regress on the Specified Multi-dimensional Point

Methods inherited from class org.drip.function.definition.RdToR1

derivative, differential, dimension, evaluate, gradient, gradientModulus, gradientModulusFunction, hessian, integrate, jacobian, maxima, minima, ValidateInput

Methods inherited from class java.lang.Object

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

Constructor Detail

RdDecisionFunction

public RdDecisionFunction(RdGeneralizedVector rdPredictor,
                          RdNormed rdInverseMargin,
                          double[] adblInverseMarginWeight,
                          double dblB)
                   throws java.lang.Exception

RdDecisionFunction Constructor

Parameters:

rdPredictor - The R^d Metric Input Predictor Space

rdInverseMargin - The Inverse Margin Weights R^d Space

adblInverseMarginWeight - Array of Inverse Margin Weights

dblB - The Kernel Offset

Throws:

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

Method Detail

predictorSpace

public RdGeneralizedVector predictorSpace()

Retrieve the Input Predictor Metric Vector Space

Returns:

The Input Predictor Metric Vector Space

inverseMarginSpace

public RdNormed inverseMarginSpace()

Retrieve the Inverse Margin Weight Metric Vector Space

Returns:

The Inverse Margin Weight Metric Vector Space

inverseMarginWeights

public double[] inverseMarginWeights()

Retrieve the Decision Kernel Weights

Returns:

The Decision Kernel Weights

offset

public double offset()

Retrieve the Offset

Returns:

The Offset

classify

public short classify(double[] adblX)
               throws java.lang.Exception

Classify the Specified Multi-dimensional Point

Parameters:

adblX - The Multi-dimensional Input Point

Returns:

+1/-1 Boolean Space Output Equivalents

Throws:

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

regress

public double regress(double[] adblX)
               throws java.lang.Exception

Regress on the Specified Multi-dimensional Point

Parameters:

adblX - The Multi-dimensional Input Point

Returns:

The Regression Output

Throws:

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

entropyNumberUpperBounds

public DecisionFunctionOperatorBounds entropyNumberUpperBounds(DiagonalScalingOperator dsoFactorizer,
                                                               double dblFeatureSpaceMaureyConstant)

Compute the Entropy Number Upper Bounds Instance for the Specified Inputs

Parameters:

dsoFactorizer - The Factorizing Diagonal Scaling Operator

dblFeatureSpaceMaureyConstant - The Feature Space Maurey Constant

Returns:

The Entropy Number Upper Bounds Instance

logEntropyNumberAsymptote

public double logEntropyNumberAsymptote(DiagonalScalingOperator dsoFactorizer)
                                 throws java.lang.Exception

Compute the Decision Function's Asymptotic Exponent for the Entropy Number

Parameters:

dsoFactorizer - The Factorizing Diagonal Scaling Operator

Returns:

The Decision Function's Asymptotic Exponent for the Entropy Number

Throws:

java.lang.Exception - Thrown if the Asymptotoc Exponent cannot be computed

optimizeRegressionHyperplane

public abstract boolean optimizeRegressionHyperplane(double[] adblEmpirical,
                                                     double dblMargin,
                                                     double dblInverseWidthNormConstraint)

Optimize the Hyper-plane for the Purposes of Regression

Parameters:

adblEmpirical - The Empirical Observation Array

dblMargin - The Optimization Margin

dblInverseWidthNormConstraint - The Inverse Width Norm Constraint

Returns:

TRUE - The Hyper-plane has been successfully Optimized for Regression

optimizeClassificationHyperplane

public abstract boolean optimizeClassificationHyperplane(short[] asEmpirical,
                                                         double dblMargin,
                                                         double dblInverseWidthNormConstraint)

Optimize the Hyper-plane for the Purposes of Classification

Parameters:

asEmpirical - The Empirical Observation Array

dblMargin - The Optimization Margin

dblInverseWidthNormConstraint - The Inverse Width Norm Constraint

Returns:

TRUE - The Hyper-plane has been successfully Optimized for Classification