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Multi-class Classifier

While some classification algorithms naturally permit the use of more than two classes, some algorithms, such as Support Vector Machines (SVM), are by nature solving a two-class problem only. These two-class (or binary) classifiers can be turned into multi-class classifiers by using different strategies, such as One-Against-Rest or One-Against-One.

oneDAL implements a Multi-Class Classifier using the One-Against-One strategy.

Multi-class classifiers, such as SVM, are based on two-class classifiers, which are integral components of the models trained with the corresponding multi-class classifier algorithms.

Details

Given \(n\) feature vectors \(x_1 = (x_{11}, \ldots, x_{1p}), \ldots, x_n = (x_{n1}, \ldots, x_{np})\) of size \(p\), the number of classes \(K\), and a vector of class labels \(y = (y_1, \ldots, y_n)\), where \(y_i \in \{0, 1, \ldots, K-1\}\), the problem is to build a multi-class classifier using a two-class (binary) classifier, such as a two-class SVM.

Training Stage

The model is trained with the One-Against-One method that uses the binary classification described in [Hsu02] as follows: For each pair of classes \((i, j)\), train a binary classifier, such as SVM. The total number of such binary classifiers is \(\frac{K(K-1)}{2}\).

Prediction Stage

Given a new feature vector \(x_i\), the classifier determines the class to which the vector belongs.

oneDAL provides two methods for class label prediction:

  • Wu method. According to the algorithm 2 for computation of the class probabilities described in [Wu04]. The library returns the index of the class with the largest probability.

  • Vote-based method. If the binary classifier predicts the feature vector to be in \(i\)-th class, the number of votes for the class i is increased by one, otherwise the vote is given to the j-th class. If two classes have equal numbers of votes, the class with the smallest index is selected.

Usage of Training Alternative

To build a Multi-class Classifier model using methods of the Model Builder class of Multi-class Classifier, complete the following steps:

  • Create a Multi-class Classifier model builder using a constructor with the required number of features and classes.

  • Use the setTwoClassClassifierModel method for each pair of classes to add the pre-trained two-class classifiers to the model. In the parameters to the method specify the classes’ indices and the pointer to the pre-trained two-class classifier for this pair of classes. You need to do this for each pair of classes, because the One-Against-One strategy is used.

  • Use the getModel method to get the trained Multi-class Classifier model.

  • Use the getStatus method to check the status of the model building process. If DAAL_NOTHROW_EXCEPTIONS macros is defined, the status report contains the list of errors that describe the problems API encountered (in case of API runtime failure).

Examples

Batch Processing

Multi-class classifier follows the general workflow described in Classification Usage Model.

Training

At the training stage, a multi-class classifier has the following parameters:

Training Parameters for Multi-class Classifier (Batch Processing)

Parameter

Default Value

Description

algorithmFPType

float

The floating-point type that the algorithm uses for intermediate computations. Can be float or double.

method

defaultDense

The computation method used by the multi-class classifier. The only training method supported so far is One-Against-One.

training

Pointer to an object of the SVM training class

Pointer to the training algorithm of the two-class classifier. By default, the SVM two-class classifier is used.

nClasses

Not applicable

The number of classes. A required parameter.

Prediction

At the prediction stage, a multi-class classifier has the following parameters:

Prediction Parameters for Multi-class Classifier (Batch Processing)

Parameter

Method

Default Value

Description

algorithmFPType

defaultDense or voteBased

float

The floating-point type that the algorithm uses for intermediate computations. Can be float or double.

pmethod

Not applicable

defaultDense

Available methods for multi-class classifier prediction stage:

  • defaultDense - the method described in [Wu04]

  • voteBased - the method based on the votes obtained from two-class classifiers.

tmethod

defaultDense or voteBased

training::oneAgainstOne

The computation method that was used to train the multi-class classifier model.

prediction

defaultDense or voteBased

Pointer to an object of the SVM prediction class

Pointer to the prediction algorithm of the two-class classifier. By default, the SVM two-class classifier is used.

nClasses

defaultDense or voteBased

Not applicable

The number of classes. A required parameter.

maxIterations

defaultDense

\(100\)

The maximal number of iterations for the algorithm.

accuracyThreshold

defaultDense

1.0e-12

The prediction accuracy.

resultsToEvaluate

voteBased

computeClassLabels

The 64-bit integer flag that specifies which extra characteristics of the decision function to compute.

Provide one of the following values to request a single characteristic or use bitwise OR to request a combination of the characteristics:

  • computeClassLabels for prediction

  • computeDecisionFunction for decisionFunction

Output

In addition to classifier output, multiclass classifier calculates the result described below. Pass the Result ID as a parameter to the methods that access the result of your algorithm. For more details, see Algorithms.

Output for Multi-class Classifier (Batch Processing)

Result ID

Result

decisionFunction

A numeric table of size \(n \times \frac{K(K-1)}{2}\) containing the results of the decision function computed for all binary models when the computeDecisionFunction option is enabled.

Note

If resultsToEvaluate does not contain computeDecisionFunction, the result of decisionFunction table is NULL.

By default, each numeric table of this result is an object of the HomogenNumericTable class, but you can define the result as an object of any class derived from NumericTable except for PackedSymmetricMatrix and PackedTriangularMatrix.

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