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SupportVectorReduction Class

Exact support vector reduction through linear dependency elimination.
Inheritance Hierarchy
SystemObject
  Accord.MachineLearning.VectorMachines.LearningBaseSupportVectorCalibrationSupportVectorMachineIKernelDouble, Double, IKernelDouble, Double
    Accord.MachineLearning.VectorMachines.LearningSupportVectorReductionBaseSupportVectorMachineIKernelDouble, Double, IKernelDouble, Double
      Accord.MachineLearning.VectorMachines.LearningSupportVectorReduction

Namespace:  Accord.MachineLearning.VectorMachines.Learning
Assembly:  Accord.MachineLearning (in Accord.MachineLearning.dll) Version: 3.8.0
Syntax
public class SupportVectorReduction : SupportVectorReductionBase<SupportVectorMachine<IKernel<double[]>, double[]>, IKernel<double[]>, double[]>
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The SupportVectorReduction type exposes the following members.

Constructors
  NameDescription
Public methodSupportVectorReduction
Initializes a new instance of the SupportVectorReduction class.
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Properties
  NameDescription
Protected propertyInput
Gets or sets the input vectors for training.
(Inherited from BaseSupportVectorCalibrationTModel, TKernel, TInput.)
Public propertyIsLinear
Gets whether the machine being learned is linear.
(Inherited from BaseSupportVectorCalibrationTModel, TKernel, TInput.)
Protected propertyKernel
Gets the machine's IKernel function.
(Inherited from BaseSupportVectorCalibrationTModel, TKernel, TInput.)
Public propertyModel
Gets the machine to be taught.
(Inherited from BaseSupportVectorCalibrationTModel, TKernel, TInput.)
Protected propertyOutput
Gets or sets the output labels for each training vector.
(Inherited from BaseSupportVectorCalibrationTModel, TKernel, TInput.)
Public propertyThreshold
Gets or sets the minimum threshold that is used to determine whether a weight will be kept in the machine or not. Default is 1e-12.
(Inherited from SupportVectorReductionBaseTModel, TKernel, TInput.)
Public propertyToken
Gets or sets a cancellation token that can be used to stop the learning algorithm while it is running.
(Inherited from BaseSupportVectorCalibrationTModel, TKernel, TInput.)
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Methods
  NameDescription
Protected methodCreate
Creates an instance of the model to be learned. Inheritors of this abstract class must define this method so new models can be created from the training data.
(Inherited from BaseSupportVectorCalibrationTModel, TKernel, TInput.)
Public methodEquals
Determines whether the specified object is equal to the current object.
(Inherited from Object.)
Protected methodFinalize
Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Protected methodInnerRun
Runs the learning algorithm.
(Inherited from SupportVectorReductionBaseTModel, TKernel, TInput.)
Public methodLearn
Learns a model that can map the given inputs to the given outputs.
(Inherited from SupportVectorReductionBaseTModel, TKernel, TInput.)
Public methodLearn(TInput, Boolean, Double)
Learns a model that can map the given inputs to the given outputs.
(Inherited from BaseSupportVectorCalibrationTModel, TKernel, TInput.)
Public methodLearn(TInput, Boolean, Double)
Learns a model that can map the given inputs to the given outputs.
(Inherited from BaseSupportVectorCalibrationTModel, TKernel, TInput.)
Public methodLearn(TInput, Double, Double)
Learns a model that can map the given inputs to the given outputs.
(Inherited from BaseSupportVectorCalibrationTModel, TKernel, TInput.)
Public methodLearn(TInput, Int32, Double)
Learns a model that can map the given inputs to the given outputs.
(Inherited from BaseSupportVectorCalibrationTModel, TKernel, TInput.)
Public methodLearn(TInput, Int32, Double)
Learns a model that can map the given inputs to the given outputs.
(Inherited from BaseSupportVectorCalibrationTModel, TKernel, TInput.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodRun Obsolete.
Obsolete.
(Inherited from SupportVectorReductionBaseTModel, TKernel, TInput.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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Extension Methods
  NameDescription
Public Extension MethodHasMethod
Checks whether an object implements a method with the given name.
(Defined by ExtensionMethods.)
Public Extension MethodIsEqual
Compares two objects for equality, performing an elementwise comparison if the elements are vectors or matrices.
(Defined by Matrix.)
Public Extension MethodTo(Type)Overloaded.
Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.)
Public Extension MethodToTOverloaded.
Converts an object into another type, irrespective of whether the conversion can be done at compile time or not. This can be used to convert generic types to numeric types during runtime.
(Defined by ExtensionMethods.)
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Examples

The following example shows how to reduce the number of support vectors in a SVM by removing vectors which are linearly dependent between themselves.

// Example AND problem
double[][] inputs =
{
    new double[] { 0, 0 }, // 0 and 0: 0 (label -1)
    new double[] { 0, 1 }, // 0 and 1: 0 (label -1)
    new double[] { 1, 0 }, // 1 and 0: 0 (label -1)
    new double[] { 1, 1 }  // 1 and 1: 1 (label +1)
};

// Dichotomy SVM outputs should be given as [-1;+1]
int[] labels =
{
    // 0,  0,  0, 1
      -1, -1, -1, 1
};

// Instantiate a new learning algorithm for SVMs
var smo = new SequentialMinimalOptimization<Linear>()
{

    // Set up the learning algorithm
    Complexity = 100.0
};

// Run
var svm = smo.Learn(inputs, labels);

int numberBefore = svm.SupportVectors.Length; // should be

double errorBefore = new ZeroOneLoss(labels).Loss(svm.Decide(inputs)); // should be 0


// At this point we have the weighted support vectors
//     w        sv        b
//   (+4)  *  (1,1)      -3
//   (-2)  *  (1,0)
//   (-2)  *  (0,1)
// 
// However, it can be seen that the last SV can be written
// as a linear combination of the two first vectors:
// 
//   (0,1) = (1,1) - (1,0)
// 
// Since we have a linear space (we are using a linear kernel)
// this vector could be removed from the support vector set.
// 
// f(x) = sum(alpha_i * x * x_i) + b
//      = 4*(1,1)*x - 2*(1,0)*x - 2*(0,1)*x             - 3
//      = 4*(1,1)*x - 2*(1,0)*x - 2*((1,1) - (1,0))*x   - 3
//      = 4*(1,1)*x - 2*(1,0)*x - 2*(1,1)*x + 2*(1,0)*x - 3
//      = 4*(1,1)*x - 2*(1,0)*x - 2*(1,1)*x + 2*(1,0)*x - 3
//      = 2*(1,1)*x - 3
//      = 2*x1 + 2*x2 - 3
// 

// Clone the original machine so we don't change it
var clone = (SupportVectorMachine<Linear>)svm.Clone();

// Create a support vector reduction algorithm
var svr = new SupportVectorReduction<Linear>(clone);

// Reduce the number of support vectors
var svm2 = svr.Learn();

int numberAfter = svm2.SupportVectors.Length; // should be 1

// Compute the new error
double errorAfter = new ZeroOneLoss(labels).Loss(svm2.Decide(inputs)); // should still be 0
See Also