Originally, support vector machines (SVM) was a technique for building an optimal binary (2-class) classifier. Later the technique was extended to regression and clustering problems. SVM is a partial case of kernel-based methods. It maps feature vectors into a higher-dimensional space using a kernel function and builds an optimal linear discriminating function in this space or an optimal hyper-plane that fits into the training data. In 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, which means that the margin between the separating hyper-plane and the nearest feature vectors from both classes (in case of 2-class classifier) is maximal. The feature vectors that are the closest to the hyper-plane are called support vectors, which means that the position of other vectors does not affect the hyper-plane (the decision function).
SVM implementation in OpenCV is based on [LibSVM].
[Burges98] |
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[LibSVM] | (1, 2) C.-C. Chang and C.-J. Lin. LIBSVM: a library for support vector machines, ACM Transactions on Intelligent Systems and Technology, 2:27:1–27:27, 2011. (http://www.csie.ntu.edu.tw/~cjlin/papers/libsvm.pdf) |
The structure represents the logarithmic grid range of statmodel parameters. It is used for optimizing statmodel accuracy by varying model parameters, the accuracy estimate being computed by cross-validation.
Minimum value of the statmodel parameter.
Maximum value of the statmodel parameter.
Logarithmic step for iterating the statmodel parameter.
The grid determines the following iteration sequence of the statmodel parameter values:
where is the maximal index satisfying
The grid is logarithmic, so step must always be greater then 1.
The constructors.
The full constructor initializes corresponding members. The default constructor creates a dummy grid:
CvParamGrid::CvParamGrid()
{
min_val = max_val = step = 0;
}
Checks validness of the grid.
Returns true if the grid is valid and false otherwise. The grid is valid if and only if:
SVM training parameters.
The structure must be initialized and passed to the training method of CvSVM.
The constructors.
Parameters: |
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The default constructor initialize the structure with following values:
CvSVMParams::CvSVMParams() :
svm_type(CvSVM::C_SVC), kernel_type(CvSVM::RBF), degree(0),
gamma(1), coef0(0), C(1), nu(0), p(0), class_weights(0)
{
term_crit = cvTermCriteria( CV_TERMCRIT_ITER+CV_TERMCRIT_EPS, 1000, FLT_EPSILON );
}
Support Vector Machines.
Note
Default and training constructors.
The constructors follow conventions of CvStatModel::CvStatModel(). See CvStatModel::train() for parameters descriptions.
Trains an SVM.
The method trains the SVM model. It follows the conventions of the generic CvStatModel::train() approach with the following limitations:
All the other parameters are gathered in the CvSVMParams structure.
Trains an SVM with optimal parameters.
Parameters: |
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The method trains the SVM model automatically by choosing the optimal parameters C, gamma, p, nu, coef0, degree from CvSVMParams. Parameters are considered optimal when the cross-validation estimate of the test set error is minimal.
If there is no need to optimize a parameter, the corresponding grid step should be set to any value less than or equal to 1. For example, to avoid optimization in gamma, set gamma_grid.step = 0, gamma_grid.min_val, gamma_grid.max_val as arbitrary numbers. In this case, the value params.gamma is taken for gamma.
And, finally, if the optimization in a parameter is required but the corresponding grid is unknown, you may call the function CvSVM::get_default_grid(). To generate a grid, for example, for gamma, call CvSVM::get_default_grid(CvSVM::GAMMA).
This function works for the 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 parameters specified in params is executed.
Predicts the response for input sample(s).
Parameters: |
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If you pass one sample then prediction result is returned. If you want to get responses for several samples then you should pass the results matrix where prediction results will be stored.
The function is parallelized with the TBB library.
Generates a grid for SVM parameters.
Parameters: |
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The function generates a grid for the specified parameter of the SVM algorithm. The grid may be passed to the function CvSVM::train_auto().
Returns the current SVM parameters.
This function may be used to get the optimal parameters obtained while automatically training CvSVM::train_auto().
Retrieves a number of support vectors and the particular vector.
Parameters: | i – Index of the particular support vector. |
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The methods can be used to retrieve a set of support vectors.