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SupportVectorMachineTKernel, TInput Class

Sparse Kernel Support Vector Machine (kSVM)
Inheritance Hierarchy
SystemObject
  Accord.MachineLearningTransformBaseTInput, Boolean
    Accord.MachineLearningClassifierBaseTInput, Boolean
      Accord.MachineLearningBinaryClassifierBaseTInput
        Accord.MachineLearningBinaryScoreClassifierBaseTInput
          Accord.MachineLearningBinaryLikelihoodClassifierBaseTInput
            Accord.MachineLearning.VectorMachinesSupportVectorMachineTKernel, TInput
              Accord.MachineLearning.VectorMachinesSupportVectorMachineTKernel

Namespace:  Accord.MachineLearning.VectorMachines
Assembly:  Accord.MachineLearning (in Accord.MachineLearning.dll) Version: 3.5.0
Syntax
[SerializableAttribute]
public class SupportVectorMachine<TKernel, TInput> : BinaryLikelihoodClassifierBase<TInput>, 
	ISupportVectorMachine<TInput>, IBinaryLikelihoodClassifier<TInput>, IBinaryScoreClassifier<TInput>, 
	IBinaryClassifier<TInput>, IMulticlassClassifier<TInput>, IMultilabelClassifier<TInput>, 
	IMultilabelClassifier<TInput, int[]>, IClassifier<TInput, int[]>, 
	ITransform<TInput, int[]>, ITransform, IMultilabelClassifier<TInput, bool[]>, 
	IClassifier<TInput, bool[]>, ITransform<TInput, bool[]>, 
	IMultilabelClassifier<TInput, double[]>, IClassifier<TInput, double[]>, 
	ITransform<TInput, double[]>, IMulticlassClassifier<TInput, int>, 
	IClassifier<TInput, int>, ITransform<TInput, int>, IMulticlassClassifier<TInput, double>, 
	IClassifier<TInput, double>, ITransform<TInput, double>, 
	IClassifier<TInput, bool>, ITransform<TInput, bool>, 
	IMulticlassOutScoreClassifier<TInput, bool>, IMulticlassScoreClassifier<TInput, bool>, 
	IMultilabelOutScoreClassifier<TInput, bool>, IMultilabelScoreClassifier<TInput, bool>, 
	IMulticlassScoreClassifier<TInput>, IMulticlassOutScoreClassifier<TInput, int>, IMulticlassScoreClassifier<TInput, int>, 
	IMultilabelOutScoreClassifier<TInput, int>, IMultilabelScoreClassifier<TInput, int>, IMulticlassOutScoreClassifier<TInput, double>, 
	IMulticlassScoreClassifier<TInput, double>, IMultilabelOutScoreClassifier<TInput, double>, 
	IMultilabelScoreClassifier<TInput, double>, IMulticlassRefScoreClassifier<TInput, int[]>, 
	IMultilabelRefScoreClassifier<TInput, int[]>, IMultilabelScoreClassifier<TInput, int[]>, 
	IMulticlassRefScoreClassifier<TInput, bool[]>, IMultilabelRefScoreClassifier<TInput, bool[]>, 
	IMultilabelScoreClassifier<TInput, bool[]>, IMulticlassRefScoreClassifier<TInput, double[]>, 
	IMultilabelRefScoreClassifier<TInput, double[]>, IMultilabelScoreClassifier<TInput, double[]>, 
	IMultilabelScoreClassifier<TInput>, IMulticlassOutLikelihoodClassifier<TInput, bool>, IMultilabelOutLikelihoodClassifier<TInput, bool>, 
	IMultilabelLikelihoodClassifier<TInput, bool>, IMulticlassLikelihoodClassifier<TInput, bool>, 
	IMulticlassLikelihoodClassifier<TInput>, IMulticlassOutLikelihoodClassifier<TInput, int>, IMultilabelOutLikelihoodClassifier<TInput, int>, 
	IMultilabelLikelihoodClassifier<TInput, int>, IMulticlassLikelihoodClassifier<TInput, int>, IMulticlassOutLikelihoodClassifier<TInput, double>, 
	IMultilabelOutLikelihoodClassifier<TInput, double>, IMultilabelLikelihoodClassifier<TInput, double>, 
	IMulticlassLikelihoodClassifier<TInput, double>, IMulticlassRefLikelihoodClassifier<TInput, int[]>, 
	IMultilabelRefLikelihoodClassifier<TInput, int[]>, IMultilabelLikelihoodClassifier<TInput, int[]>, 
	IMulticlassRefLikelihoodClassifier<TInput, bool[]>, IMultilabelRefLikelihoodClassifier<TInput, bool[]>, 
	IMultilabelLikelihoodClassifier<TInput, bool[]>, IMulticlassRefLikelihoodClassifier<TInput, double[]>, 
	IMultilabelRefLikelihoodClassifier<TInput, double[]>, IMultilabelLikelihoodClassifier<TInput, double[]>, 
	IMultilabelLikelihoodClassifier<TInput>, ICloneable
where TKernel : Object, IKernel<TInput>
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Type Parameters

TKernel
TInput

The SupportVectorMachineTKernel, TInput type exposes the following members.

Constructors
  NameDescription
Public methodSupportVectorMachineTKernel, TInput
Initializes a new instance of the SupportVectorMachineTKernel, TInput class.
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Properties
  NameDescription
Public propertyInputs Obsolete.
Gets the number of inputs accepted by this machine.
Public propertyIsCompact Obsolete.
Obsolete.
Public propertyIsProbabilistic
Gets whether this machine has been calibrated to produce probabilistic outputs (through the Probability(TInput) method).
Public propertyKernel
Gets or sets the kernel used by this machine.
Public propertyNumberOfInputs
Gets the number of inputs accepted by the model.
(Inherited from TransformBaseTInput, TOutput.)
Public propertyNumberOfOutputs
Gets the number of outputs generated by the model.
(Inherited from TransformBaseTInput, TOutput.)
Public propertySupportVectors
Gets or sets the collection of support vectors used by this machine.
Public propertyThreshold
Gets or sets the threshold (bias) term for this machine.
Public propertyWeights
Gets or sets the collection of weights used by this machine.
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Methods
  NameDescription
Public methodClone
Creates a new object that is a copy of the current instance.
Public methodCompress
If this machine has a linear kernel, compresses all support vectors into a single parameter vector.
Public methodCompute(TInput) Obsolete.
Computes the given input to produce the corresponding output.
Public methodCompute(TInput, Double) Obsolete.
Computes the given input to produce the corresponding output.
Public methodDecide(TInput)
Computes class-label decisions for a given set of input vectors.
(Inherited from ClassifierBaseTInput, TClasses.)
Public methodDecide(TInput)
Computes a class-label decision for a given input.
(Overrides ClassifierBaseTInput, TClassesDecide(TInput).)
Public methodDecide(TInput, Boolean)
Computes class-label decisions for the given input.
(Inherited from BinaryClassifierBaseTInput.)
Public methodDecide(TInput, TClasses)
Computes a class-label decision for a given input.
(Inherited from ClassifierBaseTInput, TClasses.)
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.)
Public methodLogLikelihood(TInput)
Predicts a class label vector for the given input vector, returning the log-likelihood that the input vector belongs to its predicted class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodLogLikelihood(TInput)
Predicts a class label vector for the given input vector, returning the log-likelihood that the input vector belongs to its predicted class.
(Overrides BinaryLikelihoodClassifierBaseTInputLogLikelihood(TInput).)
Public methodLogLikelihood(TInput, Boolean)
Predicts a class label for each input vector, returning the log-likelihood that each vector belongs to its predicted class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodLogLikelihood(TInput, Double)
Predicts a class label vector for the given input vector, returning the log-likelihood that the input vector belongs to its predicted class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodLogLikelihood(TInput, Boolean)
Predicts a class label vector for the given input vector, returning the log-likelihood that the input vector belongs to its predicted class.
(Overrides BinaryLikelihoodClassifierBaseTInputLogLikelihood(TInput, Boolean).)
Public methodLogLikelihood(TInput, Boolean, Double)
Predicts a class label for each input vector, returning the log-likelihood that each vector belongs to its predicted class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodLogLikelihoods(TInput, Boolean)
Predicts a class label vector for the given input vector, returning the log-likelihoods of the input vector belonging to each possible class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodLogLikelihoods(TInput, Boolean)
Predicts a class label vector for each input vector, returning the log-likelihoods of the input vector belonging to each possible class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodLogLikelihoods(TInput, Boolean, Double)
Predicts a class label vector for the given input vector, returning the log-likelihoods of the input vector belonging to each possible class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodLogLikelihoods(TInput, Boolean, Double)
Predicts a class label vector for each input vector, returning the log-likelihoods of the input vector belonging to each possible class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodProbabilities(TInput, Boolean)
Predicts a class label vector for the given input vector, returning the probabilities of the input vector belonging to each possible class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodProbabilities(TInput, Boolean)
Predicts a class label vector for each input vector, returning the probabilities of the input vector belonging to each possible class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodProbabilities(TInput, Boolean, Double)
Predicts a class label vector for the given input vector, returning the probabilities of the input vector belonging to each possible class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodProbabilities(TInput, Boolean, Double)
Predicts a class label vector for each input vector, returning the probabilities of the input vector belonging to each possible class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodProbability(TInput)
Predicts a class label for the given input vector, returning the probability that the input vector belongs to its predicted class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodProbability(TInput)
Predicts a class label for the given input vector, returning the probability that the input vector belongs to its predicted class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodProbability(TInput, Boolean)
Predicts a class label for the given input vector, returning the probability that the input vector belongs to its predicted class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodProbability(TInput, Boolean)
Predicts a class label for each input vector, returning the probability that each vector belongs to its predicted class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodProbability(TInput, Double)
Predicts a class label for the given input vector, returning the probability that the input vector belongs to its predicted class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodProbability(TInput, Boolean, Double)
Predicts a class label for each input vector, returning the probability that each vector belongs to its predicted class.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodScore(TInput)
Computes a numerical score measuring the association between the given input vector and its most strongly associated class (as predicted by the classifier).
(Inherited from BinaryScoreClassifierBaseTInput.)
Public methodScore(TInput)
Computes a numerical score measuring the association between the given input vector and its most strongly associated class (as predicted by the classifier).
(Overrides BinaryLikelihoodClassifierBaseTInputScore(TInput).)
Public methodScore(TInput, Boolean)
Predicts a class label for the input vector, returning a numerical score measuring the strength of association of the input vector to its most strongly related class.
(Inherited from BinaryScoreClassifierBaseTInput.)
Public methodScore(TInput, Boolean)
Predicts a class label for each input vector, returning a numerical score measuring the strength of association of the input vector to the most strongly related class.
(Inherited from BinaryScoreClassifierBaseTInput.)
Public methodScore(TInput, Double)
Computes a numerical score measuring the association between the given input vector and each class.
(Inherited from BinaryScoreClassifierBaseTInput.)
Public methodScore(TInput, Boolean, Double)
Predicts a class label for each input vector, returning a numerical score measuring the strength of association of the input vector to the most strongly related class.
(Inherited from BinaryScoreClassifierBaseTInput.)
Public methodScores(TInput)
Computes a numerical score measuring the association between the given input vector and each class.
(Inherited from BinaryScoreClassifierBaseTInput.)
Public methodScores(TInput)
Computes a numerical score measuring the association between the given input vector and each class.
(Inherited from BinaryScoreClassifierBaseTInput.)
Public methodScores(TInput, Boolean)
Predicts a class label vector for the given input vector, returning a numerical score measuring the strength of association of the input vector to each of the possible classes.
(Inherited from BinaryScoreClassifierBaseTInput.)
Public methodScores(TInput, Double)
Computes a numerical score measuring the association between the given input vector and each class.
(Inherited from BinaryScoreClassifierBaseTInput.)
Public methodScores(TInput, Boolean)
Predicts a class label vector for each input vector, returning a numerical score measuring the strength of association of the input vector to each of the possible classes.
(Inherited from BinaryScoreClassifierBaseTInput.)
Public methodScores(TInput, Double)
Computes a numerical score measuring the association between the given input vector and each class.
(Inherited from BinaryScoreClassifierBaseTInput.)
Public methodScores(TInput, Boolean, Double)
Predicts a class label vector for the given input vector, returning a numerical score measuring the strength of association of the input vector to each of the possible classes.
(Inherited from BinaryScoreClassifierBaseTInput.)
Public methodScores(TInput, Boolean, Double)
Predicts a class label vector for each input vector, returning a numerical score measuring the strength of association of the input vector to each of the possible classes.
(Inherited from BinaryScoreClassifierBaseTInput.)
Public methodToMulticlass
Views this instance as a multi-class generative classifier, giving access to more advanced methods, such as the prediction of integer labels.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodToMultilabel
Views this instance as a multi-label generative classifier, giving access to more advanced methods, such as the prediction of one-hot vectors.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
Public methodToWeights
Converts a Linear-kernel machine into an array of linear coefficients. The first position in the array is the Threshold value.
Public methodTransform(TInput)
Applies the transformation to an input, producing an associated output.
(Inherited from ClassifierBaseTInput, TClasses.)
Public methodTransform(TInput)
Applies the transformation to a set of input vectors, producing an associated set of output vectors.
(Inherited from TransformBaseTInput, TOutput.)
Public methodTransform(TInput, Boolean)
Applies the transformation to an input, producing an associated output.
(Inherited from BinaryClassifierBaseTInput.)
Public methodTransform(TInput, Int32)
Applies the transformation to an input, producing an associated output.
(Inherited from BinaryClassifierBaseTInput.)
Public methodTransform(TInput, Boolean)
Applies the transformation to an input, producing an associated output.
(Inherited from BinaryClassifierBaseTInput.)
Public methodTransform(TInput, Int32)
Applies the transformation to an input, producing an associated output.
(Inherited from BinaryClassifierBaseTInput.)
Public methodTransform(TInput, Int32)
Applies the transformation to an input, producing an associated output.
(Inherited from BinaryClassifierBaseTInput.)
Public methodTransform(TInput, Double)
Applies the transformation to a set of input vectors, producing an associated set of output vectors.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodTransform(TInput, Double)
Applies the transformation to a set of input vectors, producing an associated set of output vectors.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodTransform(TInput, Double)
Applies the transformation to a set of input vectors, producing an associated set of output vectors.
(Inherited from BinaryLikelihoodClassifierBaseTInput.)
Public methodTransform(TInput, TClasses)
Applies the transformation to an input, producing an associated output.
(Inherited from ClassifierBaseTInput, TClasses.)
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Operators
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 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.)
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 Matrix.)
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Remarks

The original optimal hyperplane algorithm (SVM) proposed by Vladimir Vapnik in 1963 was a linear classifier. However, in 1992, Bernhard Boser, Isabelle Guyon and Vapnik suggested a way to create non-linear classifiers by applying the kernel trick (originally proposed by Aizerman et al.) to maximum-margin hyperplanes. The resulting algorithm is formally similar, except that every dot product is replaced by a non-linear kernel function.

This allows the algorithm to fit the maximum-margin hyperplane in a transformed feature space. The transformation may be non-linear and the transformed space high dimensional; thus though the classifier is a hyperplane in the high-dimensional feature space, it may be non-linear in the original input space.

The machines are also able to learn sequence classification problems in which the input vectors can have arbitrary length. For an example on how to do that, please see the documentation page for the DynamicTimeWarping kernel.

References:

Examples

The first example shows how to learn an SVM using a standard kernel that operates on vectors of doubles.

// As an example, we will try to learn a decision machine 
// that can replicate the "exclusive-or" logical function:

double[][] inputs =
{
    new double[] { 0, 0 }, // the XOR function takes two booleans
    new double[] { 0, 1 }, // and computes their exclusive or: the
    new double[] { 1, 0 }, // output is true only if the two booleans
    new double[] { 1, 1 }  // are different
};

int[] xor = // this is the output of the xor function
{
    0, // 0 xor 0 = 0 (inputs are equal)
    1, // 0 xor 1 = 1 (inputs are different)
    1, // 1 xor 0 = 1 (inputs are different)
    0, // 1 xor 1 = 0 (inputs are equal)
};

// Now, we can create the sequential minimal optimization teacher
var learn = new SequentialMinimalOptimization<Gaussian>()
{
    UseComplexityHeuristic = true,
    UseKernelEstimation = true
};

// And then we can obtain a trained SVM by calling its Learn method
SupportVectorMachine<Gaussian> svm = learn.Learn(inputs, xor);

// Finally, we can obtain the decisions predicted by the machine:
bool[] prediction = svm.Decide(inputs);

The second example shows how to learn an SVM using a Sparse kernel that operates on sparse vectors.

// As an example, we will try to learn a decision machine 
// that can replicate the "exclusive-or" logical function:

Sparse<double>[] inputs =
{
    Sparse.FromDense(new double[] { 0, 0 }), // the XOR function takes two booleans
    Sparse.FromDense(new double[] { 0, 1 }), // and computes their exclusive or: the
    Sparse.FromDense(new double[] { 1, 0 }), // output is true only if the two booleans
    Sparse.FromDense(new double[] { 1, 1 })  // are different
};

int[] xor = // this is the output of the xor function
{
    0, // 0 xor 0 = 0 (inputs are equal)
    1, // 0 xor 1 = 1 (inputs are different)
    1, // 1 xor 0 = 1 (inputs are different)
    0, // 1 xor 1 = 0 (inputs are equal)
};

// Now, we can create the sequential minimal optimization teacher
var learn = new SequentialMinimalOptimization<Gaussian, Sparse<double>>()
{
    UseComplexityHeuristic = true,
    UseKernelEstimation = true
};

// And then we can obtain a trained SVM by calling its Learn method
var svm = learn.Learn(inputs, xor);

// Finally, we can obtain the decisions predicted by the machine:
bool[] prediction = svm.Decide(inputs);
See Also