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MulticlassSupportVectorMachineTKernel Class

One-against-one Multi-class Kernel Support Vector Machine Classifier.
Inheritance Hierarchy
SystemObject
  Accord.MachineLearningTransformBaseDouble, Int32
    Accord.MachineLearningClassifierBaseDouble, Int32
      Accord.MachineLearningMulticlassClassifierBaseDouble
        Accord.MachineLearningMulticlassScoreClassifierBaseDouble
          Accord.MachineLearningMulticlassLikelihoodClassifierBaseDouble
            Accord.MachineLearningOneVsOneSupportVectorMachineTKernel, Double
              Accord.MachineLearning.VectorMachinesMulticlassSupportVectorMachineSupportVectorMachineTKernel, TKernel, Double
                Accord.MachineLearning.VectorMachinesMulticlassSupportVectorMachineTKernel
                  Accord.MachineLearning.VectorMachinesMulticlassSupportVectorMachine

Namespace:  Accord.MachineLearning.VectorMachines
Assembly:  Accord.MachineLearning (in Accord.MachineLearning.dll) Version: 3.8.0
Syntax
[SerializableAttribute]
public class MulticlassSupportVectorMachine<TKernel> : MulticlassSupportVectorMachine<SupportVectorMachine<TKernel>, TKernel, double[]>, 
	ICloneable
where TKernel : Object, IKernel<double[]>
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Type Parameters

TKernel

The MulticlassSupportVectorMachineTKernel type exposes the following members.

Constructors
Properties
  NameDescription
Public propertyCount
Gets the number of inner binary classification models used by this instance. It should correspond to (c * (c - 1)) / 2 where c is the number of classes.
(Inherited from OneVsOneTBinary, TInput.)
Protected propertyIndices
Gets the pair of class indices handled by each inner binary classification model.
(Inherited from OneVsOneTBinary, TInput.)
Public propertyItemInt32
Gets a inner binary classification model inside this OneVsOneTBinary classifier, together with the pair of classes that it has been designed to distinguish.
(Inherited from OneVsOneTBinary, TInput.)
Public propertyItemInt32, Int32
Gets or sets the inner binary classification model used to distinguish between the given pair of classes.
(Inherited from OneVsOneTBinary, TInput.)
Public propertyKernel
Gets or sets the kernel function used in all machines at once.
(Inherited from MulticlassSupportVectorMachineTModel, TKernel, TInput.)
Protected propertyLastDecisionPath
Gets the last decision path without cloning.
(Inherited from OneVsOneTBinary, TInput.)
Public propertyMethod
Gets or sets the multi-class classification method to be used when deciding for the class of a given input vector. Default is Elimination.
(Inherited from OneVsOneTBinary, TInput.)
Public propertyModels
Gets the inner binary classification models.
(Inherited from OneVsOneTBinary, TInput.)
Public propertyNumberOfClasses
Gets the number of classes expected and recognized by the classifier.
(Inherited from ClassifierBaseTInput, TClasses.)
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 propertyParallelOptions
Gets or sets the parallelization options for this algorithm.
(Inherited from OneVsOneTBinary, TInput.)
Public propertySupportVectorCache
Gets or sets the minimum number of shared support vectors that a machine should have for kernel evaluation caching to be enabled. Default is 64.
(Inherited from MulticlassSupportVectorMachineTModel, TKernel, TInput.)
Public propertySupportVectorCount
Gets the total number of support vectors in the entire multi-class machine.
(Inherited from MulticlassSupportVectorMachineTModel, TKernel, TInput.)
Public propertySupportVectorSharedCount
Gets the number of shared support vectors in the multi-class machine.
(Inherited from MulticlassSupportVectorMachineTModel, TKernel, TInput.)
Public propertySupportVectorUniqueCount
Gets the number of unique support vectors in the multi-class machine.
(Inherited from MulticlassSupportVectorMachineTModel, TKernel, TInput.)
Public propertyToken
Gets or sets a cancellation token that can be used to cancel the algorithm while it is running.
(Inherited from OneVsOneTBinary, TInput.)
Public propertyTrack
Gets or sets whether to track the decision path associated with each decision. The track will be available through the GetLastDecisionPath method. Default is true.
(Inherited from OneVsOneTBinary, TInput.)
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Methods
  NameDescription
Public methodClone
Creates a new object that is a copy of the current instance.
(Inherited from MulticlassSupportVectorMachineTModel, TKernel, TInput.)
Public methodCompress
If the inner machines have a linear kernel, compresses their support vectors into a single parameter vector for each machine.
(Inherited from MulticlassSupportVectorMachineTModel, TKernel, TInput.)
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.
(Inherited from MulticlassSupportVectorMachineTModel, TKernel, TInput.)
Public methodDecide(TInput, Boolean)
Computes class-label decisions for the given input.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodDecide(TInput, Double)
Computes class-label decisions for the given input.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodDecide(TInput, Int32)
Computes class-label decisions for the given input.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodDecide(TInput, Double)
Computes a class-label decision for a given input.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodDecide(TInput, Int32)
Computes a class-label decision for a given input.
(Inherited from MulticlassSupportVectorMachineTModel, TKernel, TInput.)
Public methodDispose
Performs application-defined tasks associated with freeing, releasing, or resetting unmanaged resources.
(Inherited from MulticlassSupportVectorMachineTModel, TKernel, TInput.)
Protected methodDispose(Boolean)
Releases unmanaged and - optionally - managed resources
(Inherited from MulticlassSupportVectorMachineTModel, 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 methodGetClassifierForClassPair
Gets the inner binary classification model used to distinguish between the given pair of classes.
(Inherited from OneVsOneTBinary, TInput.)
Public methodGetEnumerator
Returns an enumerator that iterates through all machines contained inside this multi-class support vector machine.
(Inherited from OneVsOneTBinary, TInput.)
Public methodGetHashCode
Serves as the default hash function.
(Inherited from Object.)
Public methodGetLastDecisionPath
Gets the last decision path used during the last call to any of the model evaluation (Decide, Distance, LogLikelihood, Probability) methods in the current thread. This method is thread-safe and returns the value obtained in the last call on the current thread.
(Inherited from OneVsOneTBinary, TInput.)
Public methodGetLastKernelEvaluations
Gets the total kernel evaluations performed in the last call to Decide(TInput) and similar functions in the current thread.
(Inherited from MulticlassSupportVectorMachineTModel, TKernel, TInput.)
Public methodGetLastKernelHits
Gets the number of cache hits during in the last call to Decide(TInput) and similar functions in the current thread.
(Inherited from MulticlassSupportVectorMachineTModel, TKernel, TInput.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodLogLikelihood(TInput)
Computes the log-likelihood that the given input vector belongs to its most plausible class.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihood(TInput)
Computes the log-likelihood that the given input vectors belongs to each of the possible classes.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihood(TInput, Int32)
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 MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihood(TInput, Double)
Computes the log-likelihood that the given input vectors belongs to each of the possible classes.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihood(TInput, Int32)
Computes the log-likelihood that the given input vector belongs to the specified classIndex.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihood(TInput, Int32)
Computes the log-likelihood that the given input vector belongs to the specified classIndex.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihood(TInput, Int32)
Predicts a class label for each input vector, returning the log-likelihood that each vector belongs to its predicted class.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihood(TInput, Int32)
Computes the log-likelihood that the given input vector belongs to the specified classIndex.
(Inherited from OneVsOneTBinary, TInput.)
Public methodLogLikelihood(TInput, Int32, Double)
Computes the log-likelihood that the given input vector belongs to the specified classIndex.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihood(TInput, Int32, Double)
Computes the log-likelihood that the given input vector belongs to the specified classIndex.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihood(TInput, Int32, Double)
Predicts a class label for each input vector, returning the log-likelihood that each vector belongs to its predicted class.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihoods(TInput)
Computes the log-likelihood that the given input vector belongs to each of the possible classes.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihoods(TInput)
Computes the log-likelihood that the given input vectors belongs to each of the possible classes.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihoods(TInput, Int32)
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 MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihoods(TInput, Double)
Computes the log-likelihood that the given input vector belongs to each of the possible classes.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihoods(TInput, Int32)
Computes the log-likelihood that the given input vector belongs to the specified classIndex.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihoods(TInput, Int32)
Predicts a class label vector for each input vector, returning the log-likelihoods of the input vector belonging to each possible class.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihoods(TInput, 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 OneVsOneTBinary, TInput.)
Public methodLogLikelihoods(TInput, Int32, 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 MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihoods(TInput, Int32, Double)
Computes the log-likelihood that the given input vector belongs to the specified classIndex.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodLogLikelihoods(TInput, Int32, 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 MulticlassLikelihoodClassifierBaseTInput.)
Protected methodMemberwiseClone
Creates a shallow copy of the current Object.
(Inherited from Object.)
Public methodProbabilities(TInput)
Computes the probabilities that the given input vector belongs to each of the possible classes.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodProbabilities(TInput)
Computes the probabilities that the given input vector belongs to each of the possible classes.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodProbabilities(TInput, Double)
Computes the probabilities that the given input vector belongs to each of the possible classes.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodProbabilities(TInput, Int32)
Predicts a class label vector for the given input vector, returning the probabilities of the input vector belonging to each possible class.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodProbabilities(TInput, Double)
Computes the probabilities that the given input vector belongs to each of the possible classes.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodProbabilities(TInput, Int32)
Predicts a class label vector for each input vector, returning the probabilities of the input vector belonging to each possible class.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodProbabilities(TInput, Int32, 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 MulticlassLikelihoodClassifierBaseTInput.)
Public methodProbabilities(TInput, Int32, Double)
Predicts a class label vector for each input vector, returning the probabilities of the input vector belonging to each possible class.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
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 MulticlassLikelihoodClassifierBaseTInput.)
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 MulticlassLikelihoodClassifierBaseTInput.)
Public methodProbability(TInput, Int32)
Computes the probability that the given input vector belongs to the specified classIndex.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodProbability(TInput, Int32)
Predicts a class label for the given input vector, returning the probability that the input vector belongs to its predicted class.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
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 MulticlassLikelihoodClassifierBaseTInput.)
Public methodProbability(TInput, Int32)
Computes the probability that the given input vector belongs to the specified classIndex.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodProbability(TInput, Int32)
Computes the probability that the given input vector belongs to the specified classIndex.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodProbability(TInput, Int32)
Predicts a class label for each input vector, returning the probability that each vector belongs to its predicted class.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodProbability(TInput, Int32, Double)
Computes the probability that the given input vector belongs to the specified classIndex.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodProbability(TInput, Int32, Double)
Computes the probability that the given input vector belongs to the specified classIndex.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodProbability(TInput, Int32, Double)
Predicts a class label for each input vector, returning the probability that each vector belongs to its predicted class.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodReset
Resets the cache and machine statistics so they can be recomputed on next evaluation.
(Inherited from MulticlassSupportVectorMachineTModel, TKernel, TInput.)
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 MulticlassScoreClassifierBaseTInput.)
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 MulticlassScoreClassifierBaseTInput.)
Public methodScore(TInput, Int32)
Computes a numerical score measuring the association between the given input vector and a given classIndex.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodScore(TInput, Int32)
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 MulticlassScoreClassifierBaseTInput.)
Public methodScore(TInput, Double)
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 MulticlassScoreClassifierBaseTInput.)
Public methodScore(TInput, Int32)
Computes a numerical score measuring the association between the given input vector and a given classIndex.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Public methodScore(TInput, Int32)
Computes a numerical score measuring the association between the given input vector and a given classIndex.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Public methodScore(TInput, Int32)
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 MulticlassScoreClassifierBaseTInput.)
Public methodScore(TInput, Int32, Double)
Computes a numerical score measuring the association between the given input vector and a given classIndex.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Public methodScore(TInput, Int32, Double)
Computes a numerical score measuring the association between the given input vector and a given classIndex.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Public methodScore(TInput, Int32, 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 MulticlassScoreClassifierBaseTInput.)
Public methodScores(TInput)
Computes a numerical score measuring the association between the given input vector and each class.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Public methodScores(TInput)
Computes a numerical score measuring the association between the given input vector and each class.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Public methodScores(TInput, Int32)
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 MulticlassScoreClassifierBaseTInput.)
Public methodScores(TInput, Double)
Computes a numerical score measuring the association between the given input vector and each class.
(Inherited from MulticlassScoreClassifierBaseTInput.)
Public methodScores(TInput, Int32)
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 MulticlassScoreClassifierBaseTInput.)
Public methodScores(TInput, Double)
Computes a numerical score measuring the association between the given input vector and each class.
(Inherited from MulticlassSupportVectorMachineTModel, TKernel, TInput.)
Public methodScores(TInput, Int32, 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 MulticlassScoreClassifierBaseTInput.)
Public methodScores(TInput, Int32, 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 MulticlassScoreClassifierBaseTInput.)
Public methodToMulticlass
Views this instance as a multi-class generative classifier.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
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 MulticlassLikelihoodClassifierBaseTInput.)
Public methodToString
Returns a string that represents the current object.
(Inherited from Object.)
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, TClasses)
Applies the transformation to an input, producing an associated output.
(Inherited from ClassifierBaseTInput, TClasses.)
Public methodTransform(TInput, Boolean)
Applies the transformation to an input, producing an associated output.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodTransform(TInput, Int32)
Applies the transformation to an input, producing an associated output.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodTransform(TInput, Boolean)
Applies the transformation to an input, producing an associated output.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodTransform(TInput, Double)
Applies the transformation to an input, producing an associated output.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodTransform(TInput, Int32)
Applies the transformation to an input, producing an associated output.
(Inherited from MulticlassClassifierBaseTInput.)
Public methodTransform(TInput, Double)
Applies the transformation to an input, producing an associated output.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
Public methodTransform(TInput, Double)
Applies the transformation to an input, producing an associated output.
(Inherited from MulticlassLikelihoodClassifierBaseTInput.)
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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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Remarks

The Support Vector Machine is by nature a binary classifier. One of the ways to extend the original SVM algorithm to multiple classes is to build a one- against-one scheme where multiple SVMs specialize to recognize each of the available classes. By using a competition scheme, the original multi-class classification problem is then reduced to n*(n/2) smaller binary problems.

Currently this class supports only Kernel machines as the underlying classifiers. If a Linear Support Vector Machine is needed, specify a Linear kernel in the constructor at the moment of creation.

References:

Examples

The following example shows how to learn a linear, multi-class support vector machine using the LinearDualCoordinateDescent algorithm.

// Let's say we have the following data to be classified
// into three possible classes. Those are the samples:
// 
double[][] inputs =
{
    //               input         output
    new double[] { 0, 1, 1, 0 }, //  0 
    new double[] { 0, 1, 0, 0 }, //  0
    new double[] { 0, 0, 1, 0 }, //  0
    new double[] { 0, 1, 1, 0 }, //  0
    new double[] { 0, 1, 0, 0 }, //  0
    new double[] { 1, 0, 0, 0 }, //  1
    new double[] { 1, 0, 0, 0 }, //  1
    new double[] { 1, 0, 0, 1 }, //  1
    new double[] { 0, 0, 0, 1 }, //  1
    new double[] { 0, 0, 0, 1 }, //  1
    new double[] { 1, 1, 1, 1 }, //  2
    new double[] { 1, 0, 1, 1 }, //  2
    new double[] { 1, 1, 0, 1 }, //  2
    new double[] { 0, 1, 1, 1 }, //  2
    new double[] { 1, 1, 1, 1 }, //  2
};

int[] outputs = // those are the class labels
{
    0, 0, 0, 0, 0,
    1, 1, 1, 1, 1,
    2, 2, 2, 2, 2,
};

// Create a one-vs-one multi-class SVM learning algorithm 
var teacher = new MulticlassSupportVectorLearning<Linear>()
{
    // using LIBLINEAR's L2-loss SVC dual for each SVM
    Learner = (p) => new LinearDualCoordinateDescent()
    {
        Loss = Loss.L2
    }
};

// The following line is only needed to ensure reproducible results. Please remove it to enable full parallelization
teacher.ParallelOptions.MaxDegreeOfParallelism = 1; // (Remove, comment, or change this line to enable full parallelism)

// Learn a machine
var machine = teacher.Learn(inputs, outputs);

// Obtain class predictions for each sample
int[] predicted = machine.Decide(inputs);

// Compute classification error
double error = new ZeroOneLoss(outputs).Loss(predicted);

The following example shows how to learn a non-linear, multi-class support vector machine using the Gaussian kernel and the SequentialMinimalOptimizationTKernel algorithm.

// Let's say we have the following data to be classified
// into three possible classes. Those are the samples:
// 
double[][] inputs =
{
    //               input         output
    new double[] { 0, 1, 1, 0 }, //  0 
    new double[] { 0, 1, 0, 0 }, //  0
    new double[] { 0, 0, 1, 0 }, //  0
    new double[] { 0, 1, 1, 0 }, //  0
    new double[] { 0, 1, 0, 0 }, //  0
    new double[] { 1, 0, 0, 0 }, //  1
    new double[] { 1, 0, 0, 0 }, //  1
    new double[] { 1, 0, 0, 1 }, //  1
    new double[] { 0, 0, 0, 1 }, //  1
    new double[] { 0, 0, 0, 1 }, //  1
    new double[] { 1, 1, 1, 1 }, //  2
    new double[] { 1, 0, 1, 1 }, //  2
    new double[] { 1, 1, 0, 1 }, //  2
    new double[] { 0, 1, 1, 1 }, //  2
    new double[] { 1, 1, 1, 1 }, //  2
};

int[] outputs = // those are the class labels
{
    0, 0, 0, 0, 0,
    1, 1, 1, 1, 1,
    2, 2, 2, 2, 2,
};

// Create the multi-class learning algorithm for the machine
var teacher = new MulticlassSupportVectorLearning<Gaussian>()
{
    // Configure the learning algorithm to use SMO to train the
    //  underlying SVMs in each of the binary class subproblems.
    Learner = (param) => new SequentialMinimalOptimization<Gaussian>()
    {
        // Estimate a suitable guess for the Gaussian kernel's parameters.
        // This estimate can serve as a starting point for a grid search.
        UseKernelEstimation = true
    }
};

// The following line is only needed to ensure reproducible results. Please remove it to enable full parallelization
teacher.ParallelOptions.MaxDegreeOfParallelism = 1; // (Remove, comment, or change this line to enable full parallelism)

// Learn a machine
var machine = teacher.Learn(inputs, outputs);

// Obtain class predictions for each sample
int[] predicted = machine.Decide(inputs);

// Get class scores for each sample
double[] scores = machine.Score(inputs);

// Compute classification error
double error = new ZeroOneLoss(outputs).Loss(predicted);

Support vector machines can have their weights calibrated in order to produce probability estimates (instead of simple class separation distances). The following example shows how to use ProbabilisticOutputCalibration within MulticlassSupportVectorLearningTKernel to generate a probabilistic SVM:

// Let's say we have the following data to be classified
// into three possible classes. Those are the samples:
// 
double[][] inputs =
{
    //               input         output
    new double[] { 0, 1, 1, 0 }, //  0 
    new double[] { 0, 1, 0, 0 }, //  0
    new double[] { 0, 0, 1, 0 }, //  0
    new double[] { 0, 1, 1, 0 }, //  0
    new double[] { 0, 1, 0, 0 }, //  0
    new double[] { 1, 0, 0, 1 }, //  1
    new double[] { 0, 0, 0, 1 }, //  1
    new double[] { 0, 0, 0, 1 }, //  1
    new double[] { 1, 0, 1, 1 }, //  2
    new double[] { 1, 1, 0, 1 }, //  2
    new double[] { 0, 1, 1, 1 }, //  2
    new double[] { 1, 1, 1, 1 }, //  2
};

int[] outputs = // those are the class labels
{
    0, 0, 0, 0, 0,
    1, 1, 1,
    2, 2, 2, 2,
};

// Create the multi-class learning algorithm for the machine
var teacher = new MulticlassSupportVectorLearning<Gaussian>()
{
    // Configure the learning algorithm to use SMO to train the
    //  underlying SVMs in each of the binary class subproblems.
    Learner = (param) => new SequentialMinimalOptimization<Gaussian>()
    {
        // Estimate a suitable guess for the Gaussian kernel's parameters.
        // This estimate can serve as a starting point for a grid search.
        UseKernelEstimation = true
    }
};

// Learn a machine
var machine = teacher.Learn(inputs, outputs);


// Create the multi-class learning algorithm for the machine
var calibration = new MulticlassSupportVectorLearning<Gaussian>()
{
    Model = machine, // We will start with an existing machine

    // Configure the learning algorithm to use Platt's calibration
    Learner = (param) => new ProbabilisticOutputCalibration<Gaussian>()
    {
        Model = param.Model // Start with an existing machine
    }
};


// Configure parallel execution options
calibration.ParallelOptions.MaxDegreeOfParallelism = 1;

// Learn a machine
calibration.Learn(inputs, outputs);

// Obtain class predictions for each sample
int[] predicted = machine.Decide(inputs);

// Get class scores for each sample
double[] scores = machine.Score(inputs);

// Get log-likelihoods (should be same as scores)
double[][] logl = machine.LogLikelihoods(inputs);

// Get probability for each sample
double[][] prob = machine.Probabilities(inputs);

// Compute classification error
double error = new ZeroOneLoss(outputs).Loss(predicted);
double loss = new CategoryCrossEntropyLoss(outputs).Loss(prob);
See Also