Trains a Support Vector Machines (SVM) classifier.

The type double function is imsls_d_support_vector_trainer.

A pointer to a structure of type Imsls_f_svm_model containing the trained support vector classifier model. If training is unsuccessful, NULL is returned. To release this space, use imsls_f_svm_classifier_free.

Function imsls_f_support_vector_trainer trains an SVM classifier for classifying data into one of n_classes target classes. There are several SVM formulations that are supported through the optional arguments for classification, regression, and distribution estimation. The C-support vector classification (C-SVC) is the fundamental algorithm for the SVM optimization problem and its primal form is given as

Where (xi, yi) are the instance-label pairs for a given training set, where l is the number of training examples, and xi ∈ Rn and yi ∈ {1,-1}. ξi are the slack variables in optimization and is an upper bound on the number of errors. The regularization parameter C > 0 acts as a tradeoff parameter between error and margin. This is the default algorithm used and can be controlled through the use of the IMSLS_SVM_C_SVC_TYPE optional argument.

The ν-support vector classification (ν-SVC) algorithm presents a new parameter ν ∈ (0,1] which acts as an upper bound on the fraction of training errors and a lower bound on the fraction of support vectors. The use of this algorithm is triggered through the use of the IMSLS_SVM_NU_SVC_TYPE optional arguement. The primal optimization problem for the binary variable y ∈ {1,-1} is

The one-class SVM algorithm estimates the support of a high-dimensional distribution without any class information. Control of this algorithm is through the use of the IMSLS_SVM_ONE_CLASS_TYPE optional argument. The primal problem of one-class SVM is

If zi is the target output and given the parameters C > 0, ɛ > 0, the standard form of ɛ-support vector regression (ɛ-SVR) is

where the two slack variables ξi and ξi* are introduced, one for exceeding the target value by more than ɛ and the other for being more than ɛ below the target. The use of this algorithm is triggered through the use of the IMSLS_SVM_EPSILON_SVR_TYPE optional argument.

Similar to ν-SVC, in ν-support vector regression (ν-SVR) the parameter ν ∈ (0,1] controls the number of support vectors. Use IMSLS_SVM_NU_SVR_TYPE to trigger this algorithm. The ν-SVR primal problem is

The decomposition method used to solve the dual formulation of these primal problems is an SMO-type (sequential minimal optimization) decomposition method proposed by Fan et. al. (2005).

The IMSLS_SVM_CROSS_VALIDATION optional argument allows one to estimate how accurately the resulting training model will perform in practice. The cross validation technique partitions the training data into n_folds complementary subsets. Each of the subsets is subsequently used in training and validated against the remaining subsets. The validation results of the rounds are then averaged. The result is usually a good indicator of how the trained model will perform on unclassified data.

Function imsls_f_support_vector_trainer is based on LIBSVM, Copyright (c) 2000-2013, with permission from the authors, Chih-Chung Chang and Chih-Jen Lin, with the following disclaimer:

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In this example, we use a subset of the Fisher Iris data to train the classifier. The default values of imsls_f_support_vector_trainer are used in the training. The resultant classifier model, stored in svm_classifier, is then used as input to imsls_f_support_vector_classification to classify all of the patterns in the Fisher Iris data set. Results of the classification are then printed. In the Fisher Iris data set, the first column is the target classification value, 1=Setosa, 2=Versicolour, and 3=Virginica. Columns 2 through 5 contain the attributes sepal length, sepal width, petal length, and petal width.

In this example we use a subset of the Fisher Iris data to train the classifier and use the cross-validation option with various combinations of C and gamma to find a combination which yields the best results on the training data. The best combination of C and gamma are then used to get the classification model, stored in svm_classifier. This model is then used as input to imsls_f_support_vector_classification to classify all of the patterns in the Fisher Iris data set. Results of the classification are then printed.

One thousand uniform deviates from a uniform distribution are used in the training data set of this example. IMSLS_SVM_ONE_CLASS_TYPE is used to produce the model during training. A test data set of one hundred uniform deviates is produced and contaminated with ten normal deviates. imsls_f_support_vector_classification is then called in an attempt to pick out the contaminated data in the test data set. The suspect observations are printed.

This example uses IMSLS_SVM_NU_SVR_TYPE to create a regression model which is used by imsls_f_support_vector_classification in an attempt to predict values in the test data set. The predicted values are printed.