Originally, support vector machines (SVM) was a technique for building an optimal (in some sense) binary (2-class) classifier. Then the technique has been extended to regression and clustering problems. SVM is a partial case of kernel-based methods, it maps feature vectors into higher-dimensional space using some kernel function, and then it builds an optimal linear discriminating function in this space (or an optimal hyper-plane that fits into the training data, ...). in the case of SVM the kernel is not defined explicitly. Instead, a distance between any 2 points in the hyper-space needs to be defined.
The solution is optimal in a sense that the margin between the separating hyper-plane and the nearest feature vectors from the both classes (in the case of 2-class classifier) is maximal. The feature vectors that are the closest to the hyper-plane are called "support vectors", meaning that the position of other vectors does not affect the hyper-plane (the decision function).
There are a lot of good references on SVM. Here are only a few ones to start with.
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**[Burges98] C. Burges. "A tutorial on support vector machines for pattern recognition", Knowledge Discovery and Data Mining 2(2), 1998.**
The method trains the SVM model. It follows the conventions of the generic ``train`` "method" with the following limitations: only the CV_ROW_SAMPLE data layout is supported, the input variables are all ordered, the output variables can be either categorical ( ``_params.svm_type=CvSVM::C_SVC`` or ``_params.svm_type=CvSVM::NU_SVC`` ), or ordered ( ``_params.svm_type=CvSVM::EPS_SVR`` or ``_params.svm_type=CvSVM::NU_SVR`` ), or not required at all ( ``_params.svm_type=CvSVM::ONE_CLASS`` ), missing measurements are not supported.
:param k_fold:Cross-validation parameter. The training set is divided into ``k_fold`` subsets, one subset being used to train the model, the others forming the test set. So, the SVM algorithm is executed ``k_fold`` times.
If there is no need in optimization in some parameter, the according grid step should be set to any value less or equal to 1. For example, to avoid optimization in ``gamma`` one should set ``gamma_grid.step = 0``,``gamma_grid.min_val``,``gamma_grid.max_val`` being arbitrary numbers. In this case, the value ``params.gamma`` will be taken for ``gamma`` .
This function works for the case of classification
( ``params.svm_type=CvSVM::C_SVC`` or ``params.svm_type=CvSVM::NU_SVC`` )
as well as for the regression
( ``params.svm_type=CvSVM::EPS_SVR`` or ``params.svm_type=CvSVM::NU_SVR`` ). If ``params.svm_type=CvSVM::ONE_CLASS`` , no optimization is made and the usual SVM with specified in ``params`` parameters is executed.
