com.imsl.datamining.supportvectormachine

Class SVRegression

java.lang.Object

com.imsl.datamining.PredictiveModel

com.imsl.datamining.supportvectormachine.SupportVectorMachine

com.imsl.datamining.supportvectormachine.SVRegression

All Implemented Interfaces:

Serializable, Cloneable

public class SVRegression
extends SupportVectorMachine
implements Serializable, Cloneable

Specifies a support vector machine for regression (SVR).

The standard form SVR is the so-called epsilon-support vector regression, or \(\varepsilon\)-SVR. If \(z_i\) is the target output, then given the parameters \(C > \, 0, \varepsilon > \, 0\), the standard form SVR is

$$\min_ {w, b, \xi, \xi^*} \frac{1}{2} w^Tw+C\sum_{i=1}^{l} \xi _i + C\sum_{i=1}^{l} {\xi _i}^*$$

$$\text{subject to} \, \, w^T \phi (x_i)+b-z_i \leq \varepsilon +\xi _i,$$

$$z_i - w^T \phi (x_i)-b \leq \varepsilon +{\xi _i}^*,$$

$$ \xi_i, {\xi_i}^* \geq 0, i=1, \ldots, l $$

The variables \(\xi _i\) and \({\xi _i}^*\) are two slack variables, one for exceeding the target value by more than \(\epsilon\) and the other for being more than \(\epsilon\) below the target. \(\epsilon\) is controlled through the use of the set method setInsensitivityBand.

See Also:

Example 1, Example 2, Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class com.imsl.datamining.supportvectormachine.SupportVectorMachine

SupportVectorMachine.ReflectiveOperationException

Nested classes/interfaces inherited from class com.imsl.datamining.PredictiveModel

PredictiveModel.CloneNotSupportedException, PredictiveModel.PredictiveModelException, PredictiveModel.StateChangeException, PredictiveModel.SumOfProbabilitiesNotOneException, PredictiveModel.VariableType

Constructor Summary

Constructors

Constructor and Description
SVRegression(double[][] xy, int responseColumnIndex, PredictiveModel.VariableType[] varType) Constructs a support vector machine for regression (SVR).
SVRegression(double[][] xy, int responseColumnIndex, PredictiveModel.VariableType[] varType, Kernel k) Constructs a support vector machine for regression (SVR).
SVRegression(SVRegression svrModel) Constructs a copy of the input SVRegression predictive model.

Method Summary

Modifier and Type	Method and Description
SVRegression	clone() Clones an SVRegression predictive model.
double	getInsensitivityBand() Returns the insensitivity band parameter, \(\epsilon\), in the standard formulation of the SVM regression problem.
protected SVModel	optimize(DataNode[][] x, double[] y, double[] w, int len, Kernel kernel) Performs the regression support vector machine optimization problem.
protected double[]	predictValues(SVModel model, double[][] attributeData) Generates the predicted values on the attribute data using the given support vector machine model.
protected void	setConfiguration(PredictiveModel pm) Sets the configuration to that of the input PredictiveModel.
void	setInsensitivityBand(double epsilon) Sets the insensitivity band parameter, \(\epsilon\), in the standard formulation of the SVM regression problem.

Methods inherited from class com.imsl.datamining.supportvectormachine.SupportVectorMachine

fitModel, getConvergenceTolerance, getKernel, getKernelParameters, getModel, getNuParameter, getRegularizationParameter, getWorkingArraySize, isNuFormulation, isProbability, isShrinking, predict, predict, setConvergenceTolerance, setKernel, setKernelParameters, setNuFormulation, setNuParameter, setProbability, setRegularizationParameter, setShrinking, setWorkArraySize

Methods inherited from class com.imsl.datamining.PredictiveModel

getClassCounts, getClassErrors, getClassErrors, getClassLabels, getClassProbabilities, getCostMatrix, getMaxNumberOfCategories, getMaxNumberOfIterations, getNumberOfClasses, getNumberOfColumns, getNumberOfMissing, getNumberOfPredictors, getNumberOfRows, getNumberOfUniquePredictorValues, getPredictorIndexes, getPredictorTypes, getPrintLevel, getPriorProbabilities, getRandomObject, getResponseColumnIndex, getResponseVariableAverage, getResponseVariableMostFrequentClass, getResponseVariableType, getTotalWeight, getVariableType, getWeights, getXY, isConstantSeries, isMustFitModel, isUserFixedNClasses, predict, setClassCounts, setClassLabels, setClassProbabilities, setCostMatrix, setMaxNumberOfCategories, setMaxNumberOfIterations, setMustFitModel, setNumberOfClasses, setPredictorIndex, setPredictorTypes, setPrintLevel, setPriorProbabilities, setRandomObject, setResponseColumnIndex, setTrainingData, setVariableType, setWeights

Methods inherited from class java.lang.Object

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

Constructor Detail

SVRegression

public SVRegression(double[][] xy,
                    int responseColumnIndex,
                    PredictiveModel.VariableType[] varType)

Constructs a support vector machine for regression (SVR).

Parameters:

xy - a double matrix containing the training data and associated response values

responseColumnIndex - an int specifying the column index of the response variable

varType - a PredictiveModel.VariableType array of length equal to xy[0].length containing the type of each variable

SVRegression

public SVRegression(SVRegression svrModel)

Constructs a copy of the input SVRegression predictive model.

Parameters:

svrModel - an SVRegression predictive model

SVRegression

public SVRegression(double[][] xy,
                    int responseColumnIndex,
                    PredictiveModel.VariableType[] varType,
                    Kernel k)

Constructs a support vector machine for regression (SVR).

Parameters:

xy - a double matrix containing the training data and associated response values

responseColumnIndex - an int specifying the column index of the response variable

varType - a PredictiveModel.VariableType array of length equal to xy[0].length containing the type of each variable

k - a Kernel, the kernel function

Method Detail

clone

public SVRegression clone()

Clones an SVRegression predictive model.

Specified by:

clone in class PredictiveModel

Returns:

a clone of the SVRegression predictive model

setConfiguration

protected final void setConfiguration(PredictiveModel pm)

Sets the configuration to that of the input PredictiveModel.

Note that the input PredictiveModel object must be the same subclass of PredictiveModel as is this instance.

Overrides:

setConfiguration in class SupportVectorMachine

Parameters:

pm - a SVRegression instance

Default: The class uses its default configuration as described in the different methods.

getInsensitivityBand

public double getInsensitivityBand()

Returns the insensitivity band parameter, \(\epsilon\), in the standard formulation of the SVM regression problem.

Returns:

a double, the value of the insensitivity band parameter

setInsensitivityBand

public void setInsensitivityBand(double epsilon)

Sets the insensitivity band parameter, \(\epsilon\), in the standard formulation of the SVM regression problem.

Parameters:

epsilon - a double > 0.0, the value of the infeasibility band parameter

Default: epsilon=0.1

optimize

protected SVModel optimize(DataNode[][] x,
                           double[] y,
                           double[] w,
                           int len,
                           Kernel kernel)
                    throws NoSuchMethodException,
                           InstantiationException,
                           IllegalAccessException,
                           InvocationTargetException

Performs the regression support vector machine optimization problem.

Specified by:

optimize in class SupportVectorMachine

Parameters:

x - a DataNode matrix containing the attribute data

y - a double array containing the response variable

len - an int, the total possible number of support vectors

w - a double array containing the observation weights

kernel - a Kernel object

Returns:

an SVModel structure containing the fitted model

Throws:

NoSuchMethodException - thrown when a particular method cannot be found

InstantiationException - thrown when an application tries to create an instance of a class using the newInstance method in class Class, but the specified class object cannot be instantiated

IllegalAccessException - thrown when an application tries to reflectively create an instance (other than an array), set or get a field, or invoke a method, but the currently executing method does not have access to the definition of the specified class, field, method or constructor

InvocationTargetException - a checked exception that wraps an exception thrown by an invoked method or constructor

predictValues

protected double[] predictValues(SVModel model,
                                 double[][] attributeData)
                          throws PredictiveModel.SumOfProbabilitiesNotOneException

Generates the predicted values on the attribute data using the given support vector machine model.

Specified by:

predictValues in class SupportVectorMachine

Parameters:

model - a fitted SVModel object

attributeData - a double matrix containing the attribute (or predictor) data

Returns:

a double array containing the predictions for each row in the input attribute data

Throws:

PredictiveModel.SumOfProbabilitiesNotOneException - the sum of probabilities is not approximately one