mirror of
https://github.com/opencv/opencv.git
synced 2024-12-15 09:49:13 +08:00
317 lines
15 KiB
ReStructuredText
317 lines
15 KiB
ReStructuredText
Support Vector Machines
|
|
=======================
|
|
|
|
.. highlight:: cpp
|
|
|
|
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] C. Burges. *A tutorial on support vector machines for pattern recognition*, Knowledge Discovery and Data Mining 2(2), 1998 (available online at http://citeseer.ist.psu.edu/burges98tutorial.html)
|
|
|
|
.. [LibSVM] 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)
|
|
|
|
|
|
CvParamGrid
|
|
-----------
|
|
.. ocv:struct:: CvParamGrid
|
|
|
|
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.
|
|
|
|
.. ocv:member:: double CvParamGrid::min_val
|
|
|
|
Minimum value of the statmodel parameter.
|
|
|
|
.. ocv:member:: double CvParamGrid::max_val
|
|
|
|
Maximum value of the statmodel parameter.
|
|
|
|
.. ocv:member:: double CvParamGrid::step
|
|
|
|
Logarithmic step for iterating the statmodel parameter.
|
|
|
|
The grid determines the following iteration sequence of the statmodel parameter values:
|
|
|
|
.. math::
|
|
|
|
(min\_val, min\_val*step, min\_val*{step}^2, \dots, min\_val*{step}^n),
|
|
|
|
where :math:`n` is the maximal index satisfying
|
|
|
|
.. math::
|
|
|
|
\texttt{min\_val} * \texttt{step} ^n < \texttt{max\_val}
|
|
|
|
The grid is logarithmic, so ``step`` must always be greater then 1.
|
|
|
|
CvParamGrid::CvParamGrid
|
|
------------------------
|
|
The constructors.
|
|
|
|
.. ocv:function:: CvParamGrid::CvParamGrid()
|
|
|
|
.. ocv:function:: CvParamGrid::CvParamGrid( double min_val, double max_val, double log_step )
|
|
|
|
The full constructor initializes corresponding members. The default constructor creates a dummy grid:
|
|
|
|
::
|
|
|
|
CvParamGrid::CvParamGrid()
|
|
{
|
|
min_val = max_val = step = 0;
|
|
}
|
|
|
|
CvParamGrid::check
|
|
------------------
|
|
Checks validness of the grid.
|
|
|
|
.. ocv:function:: bool CvParamGrid::check()
|
|
|
|
Returns ``true`` if the grid is valid and ``false`` otherwise. The grid is valid if and only if:
|
|
|
|
* Lower bound of the grid is less then the upper one.
|
|
* Lower bound of the grid is positive.
|
|
* Grid step is greater then 1.
|
|
|
|
CvSVMParams
|
|
-----------
|
|
.. ocv:struct:: CvSVMParams
|
|
|
|
SVM training parameters.
|
|
|
|
The structure must be initialized and passed to the training method of :ocv:class:`CvSVM`.
|
|
|
|
CvSVMParams::CvSVMParams
|
|
------------------------
|
|
The constructors.
|
|
|
|
.. ocv:function:: CvSVMParams::CvSVMParams()
|
|
|
|
.. ocv:function:: CvSVMParams::CvSVMParams( int svm_type, int kernel_type, double degree, double gamma, double coef0, double Cvalue, double nu, double p, CvMat* class_weights, CvTermCriteria term_crit )
|
|
|
|
:param svm_type: Type of a SVM formulation. Possible values are:
|
|
|
|
* **CvSVM::C_SVC** C-Support Vector Classification. ``n``-class classification (``n`` :math:`\geq` 2), allows imperfect separation of classes with penalty multiplier ``C`` for outliers.
|
|
|
|
* **CvSVM::NU_SVC** :math:`\nu`-Support Vector Classification. ``n``-class classification with possible imperfect separation. Parameter :math:`\nu` (in the range 0..1, the larger the value, the smoother the decision boundary) is used instead of ``C``.
|
|
|
|
* **CvSVM::ONE_CLASS** Distribution Estimation (One-class SVM). All the training data are from the same class, SVM builds a boundary that separates the class from the rest of the feature space.
|
|
|
|
* **CvSVM::EPS_SVR** :math:`\epsilon`-Support Vector Regression. The distance between feature vectors from the training set and the fitting hyper-plane must be less than ``p``. For outliers the penalty multiplier ``C`` is used.
|
|
|
|
* **CvSVM::NU_SVR** :math:`\nu`-Support Vector Regression. :math:`\nu` is used instead of ``p``.
|
|
|
|
See [LibSVM]_ for details.
|
|
|
|
:param kernel_type: Type of a SVM kernel. Possible values are:
|
|
|
|
* **CvSVM::LINEAR** Linear kernel. No mapping is done, linear discrimination (or regression) is done in the original feature space. It is the fastest option. :math:`K(x_i, x_j) = x_i^T x_j`.
|
|
|
|
* **CvSVM::POLY** Polynomial kernel: :math:`K(x_i, x_j) = (\gamma x_i^T x_j + coef0)^{degree}, \gamma > 0`.
|
|
|
|
* **CvSVM::RBF** Radial basis function (RBF), a good choice in most cases. :math:`K(x_i, x_j) = e^{-\gamma ||x_i - x_j||^2}, \gamma > 0`.
|
|
|
|
* **CvSVM::SIGMOID** Sigmoid kernel: :math:`K(x_i, x_j) = \tanh(\gamma x_i^T x_j + coef0)`.
|
|
|
|
* **CvSVM::CHI2** Exponential Chi2 kernel, similar to the RBF kernel: :math:`K(x_i, x_j) = e^{-\gamma \chi^2(x_i,x_j)}, \chi^2(x_i,x_j) = (x_i-x_j)^2/(x_i+x_j), \gamma > 0`.
|
|
|
|
* **CvSVM::INTER** Histogram intersection kernel. A fast kernel. :math:`K(x_i, x_j) = min(x_i,x_j)`.
|
|
|
|
:param degree: Parameter ``degree`` of a kernel function (POLY).
|
|
|
|
:param gamma: Parameter :math:`\gamma` of a kernel function (POLY / RBF / SIGMOID / CHI2).
|
|
|
|
:param coef0: Parameter ``coef0`` of a kernel function (POLY / SIGMOID).
|
|
|
|
:param Cvalue: Parameter ``C`` of a SVM optimization problem (C_SVC / EPS_SVR / NU_SVR).
|
|
|
|
:param nu: Parameter :math:`\nu` of a SVM optimization problem (NU_SVC / ONE_CLASS / NU_SVR).
|
|
|
|
:param p: Parameter :math:`\epsilon` of a SVM optimization problem (EPS_SVR).
|
|
|
|
:param class_weights: Optional weights in the C_SVC problem , assigned to particular classes. They are multiplied by ``C`` so the parameter ``C`` of class ``#i`` becomes :math:`class\_weights_i * C`. Thus these weights affect the misclassification penalty for different classes. The larger weight, the larger penalty on misclassification of data from the corresponding class.
|
|
|
|
:param term_crit: Termination criteria of the iterative SVM training procedure which solves a partial case of constrained quadratic optimization problem. You can specify tolerance and/or the maximum number of iterations.
|
|
|
|
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 );
|
|
}
|
|
|
|
A comparison of different kernels on the following 2D test case with four classes. Four C_SVC SVMs have been trained (one against rest) with auto_train. Evaluation on three different kernels (CHI2, INTER, RBF). The color depicts the class with max score. Bright means max-score > 0, dark means max-score < 0.
|
|
|
|
.. image:: pics/SVM_Comparison.png
|
|
|
|
|
|
|
|
CvSVM
|
|
-----
|
|
.. ocv:class:: CvSVM : public CvStatModel
|
|
|
|
Support Vector Machines.
|
|
|
|
.. note::
|
|
|
|
* (Python) An example of digit recognition using SVM can be found at opencv_source/samples/python2/digits.py
|
|
* (Python) An example of grid search digit recognition using SVM can be found at opencv_source/samples/python2/digits_adjust.py
|
|
* (Python) An example of video digit recognition using SVM can be found at opencv_source/samples/python2/digits_video.py
|
|
|
|
CvSVM::CvSVM
|
|
------------
|
|
Default and training constructors.
|
|
|
|
.. ocv:function:: CvSVM::CvSVM()
|
|
|
|
.. ocv:function:: CvSVM::CvSVM( const Mat& trainData, const Mat& responses, const Mat& varIdx=Mat(), const Mat& sampleIdx=Mat(), CvSVMParams params=CvSVMParams() )
|
|
|
|
.. ocv:function:: CvSVM::CvSVM( const CvMat* trainData, const CvMat* responses, const CvMat* varIdx=0, const CvMat* sampleIdx=0, CvSVMParams params=CvSVMParams() )
|
|
|
|
.. ocv:pyfunction:: cv2.SVM([trainData, responses[, varIdx[, sampleIdx[, params]]]]) -> <SVM object>
|
|
|
|
The constructors follow conventions of :ocv:func:`CvStatModel::CvStatModel`. See :ocv:func:`CvStatModel::train` for parameters descriptions.
|
|
|
|
CvSVM::train
|
|
------------
|
|
Trains an SVM.
|
|
|
|
.. ocv:function:: bool CvSVM::train( const Mat& trainData, const Mat& responses, const Mat& varIdx=Mat(), const Mat& sampleIdx=Mat(), CvSVMParams params=CvSVMParams() )
|
|
|
|
.. ocv:function:: bool CvSVM::train( const CvMat* trainData, const CvMat* responses, const CvMat* varIdx=0, const CvMat* sampleIdx=0, CvSVMParams params=CvSVMParams() )
|
|
|
|
.. ocv:pyfunction:: cv2.SVM.train(trainData, responses[, varIdx[, sampleIdx[, params]]]) -> retval
|
|
|
|
The method trains the SVM model. It follows the conventions of the generic :ocv:func:`CvStatModel::train` approach with the following limitations:
|
|
|
|
* Only the ``CV_ROW_SAMPLE`` data layout is supported.
|
|
|
|
* Input variables are all ordered.
|
|
|
|
* 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.
|
|
|
|
All the other parameters are gathered in the
|
|
:ocv:class:`CvSVMParams` structure.
|
|
|
|
|
|
CvSVM::train_auto
|
|
-----------------
|
|
Trains an SVM with optimal parameters.
|
|
|
|
.. ocv:function:: bool CvSVM::train_auto( const Mat& trainData, const Mat& responses, const Mat& varIdx, const Mat& sampleIdx, CvSVMParams params, int k_fold = 10, CvParamGrid Cgrid = CvSVM::get_default_grid(CvSVM::C), CvParamGrid gammaGrid = CvSVM::get_default_grid(CvSVM::GAMMA), CvParamGrid pGrid = CvSVM::get_default_grid(CvSVM::P), CvParamGrid nuGrid = CvSVM::get_default_grid(CvSVM::NU), CvParamGrid coeffGrid = CvSVM::get_default_grid(CvSVM::COEF), CvParamGrid degreeGrid = CvSVM::get_default_grid(CvSVM::DEGREE), bool balanced=false)
|
|
|
|
.. ocv:function:: bool CvSVM::train_auto( const CvMat* trainData, const CvMat* responses, const CvMat* varIdx, const CvMat* sampleIdx, CvSVMParams params, int kfold = 10, CvParamGrid Cgrid = get_default_grid(CvSVM::C), CvParamGrid gammaGrid = get_default_grid(CvSVM::GAMMA), CvParamGrid pGrid = get_default_grid(CvSVM::P), CvParamGrid nuGrid = get_default_grid(CvSVM::NU), CvParamGrid coeffGrid = get_default_grid(CvSVM::COEF), CvParamGrid degreeGrid = get_default_grid(CvSVM::DEGREE), bool balanced=false )
|
|
|
|
.. ocv:pyfunction:: cv2.SVM.train_auto(trainData, responses, varIdx, sampleIdx, params[, k_fold[, Cgrid[, gammaGrid[, pGrid[, nuGrid[, coeffGrid[, degreeGrid[, balanced]]]]]]]]) -> retval
|
|
|
|
:param k_fold: Cross-validation parameter. The training set is divided into ``k_fold`` subsets. One subset is used to test the model, the others form the train set. So, the SVM algorithm is executed ``k_fold`` times.
|
|
|
|
:param \*Grid: Iteration grid for the corresponding SVM parameter.
|
|
|
|
:param balanced: If ``true`` and the problem is 2-class classification then the method creates more balanced cross-validation subsets that is proportions between classes in subsets are close to such proportion in the whole train dataset.
|
|
|
|
The method trains the SVM model automatically by choosing the optimal
|
|
parameters ``C``, ``gamma``, ``p``, ``nu``, ``coef0``, ``degree`` from
|
|
:ocv:class:`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 :ocv:func:`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.
|
|
|
|
CvSVM::predict
|
|
--------------
|
|
Predicts the response for input sample(s).
|
|
|
|
.. ocv:function:: float CvSVM::predict( const Mat& sample, bool returnDFVal=false ) const
|
|
|
|
.. ocv:function:: float CvSVM::predict( const CvMat* sample, bool returnDFVal=false ) const
|
|
|
|
.. ocv:function:: float CvSVM::predict( const CvMat* samples, CvMat* results, bool returnDFVal=false ) const
|
|
|
|
.. ocv:pyfunction:: cv2.SVM.predict(sample[, returnDFVal]) -> retval
|
|
|
|
.. ocv:pyfunction:: cv2.SVM.predict_all(samples[, results]) -> results
|
|
|
|
:param sample: Input sample for prediction.
|
|
|
|
:param samples: Input samples for prediction.
|
|
|
|
:param returnDFVal: Specifies a type of the return value. If ``true`` and the problem is 2-class classification then the method returns the decision function value that is signed distance to the margin, else the function returns a class label (classification) or estimated function value (regression).
|
|
|
|
:param results: Output prediction responses for corresponding samples.
|
|
|
|
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.
|
|
|
|
|
|
CvSVM::get_default_grid
|
|
-----------------------
|
|
Generates a grid for SVM parameters.
|
|
|
|
.. ocv:function:: CvParamGrid CvSVM::get_default_grid( int param_id )
|
|
|
|
:param param_id: SVM parameters IDs that must be one of the following:
|
|
|
|
* **CvSVM::C**
|
|
|
|
* **CvSVM::GAMMA**
|
|
|
|
* **CvSVM::P**
|
|
|
|
* **CvSVM::NU**
|
|
|
|
* **CvSVM::COEF**
|
|
|
|
* **CvSVM::DEGREE**
|
|
|
|
The grid is generated for the parameter with this ID.
|
|
|
|
The function generates a grid for the specified parameter of the SVM algorithm. The grid may be passed to the function :ocv:func:`CvSVM::train_auto`.
|
|
|
|
CvSVM::get_params
|
|
-----------------
|
|
Returns the current SVM parameters.
|
|
|
|
.. ocv:function:: CvSVMParams CvSVM::get_params() const
|
|
|
|
This function may be used to get the optimal parameters obtained while automatically training :ocv:func:`CvSVM::train_auto`.
|
|
|
|
CvSVM::get_support_vector
|
|
--------------------------
|
|
Retrieves a number of support vectors and the particular vector.
|
|
|
|
.. ocv:function:: int CvSVM::get_support_vector_count() const
|
|
|
|
.. ocv:function:: const float* CvSVM::get_support_vector(int i) const
|
|
|
|
.. ocv:pyfunction:: cv2.SVM.get_support_vector_count() -> retval
|
|
|
|
:param i: Index of the particular support vector.
|
|
|
|
The methods can be used to retrieve a set of support vectors.
|
|
|
|
CvSVM::get_var_count
|
|
--------------------
|
|
Returns the number of used features (variables count).
|
|
|
|
.. ocv:function:: int CvSVM::get_var_count() const
|
|
|
|
.. ocv:pyfunction:: cv2.SVM.get_var_count() -> retval
|