opencv/modules/ml/doc/support_vector_machines.rst
2011-06-16 12:48:23 +00:00

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Support Vector Machines
=======================
.. highlight:: cpp
Originally, support vector machines (SVM) was a technique for building an optimal binary (2-class) classifier. Later the technique has been 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).
There are a lot of good references on SVM. You may consider starting with the following:
*
[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
).
*
Chih-Chung Chang and Chih-Jen Lin. *LIBSVM - A Library for Support Vector Machines*
(
http://www.csie.ntu.edu.tw/~cjlin/libsvm/
)
.. index:: CvSVM
.. _CvSVM:
CvSVM
-----
.. c:type:: CvSVM
Support Vector Machines ::
class CvSVM : public CvStatModel
{
public:
// SVM type
enum { C_SVC=100, NU_SVC=101, ONE_CLASS=102, EPS_SVR=103, NU_SVR=104 };
// SVM kernel type
enum { LINEAR=0, POLY=1, RBF=2, SIGMOID=3 };
// SVM params type
enum { C=0, GAMMA=1, P=2, NU=3, COEF=4, DEGREE=5 };
CvSVM();
virtual ~CvSVM();
CvSVM( const Mat& _train_data, const Mat& _responses,
const Mat& _var_idx=Mat(), const Mat& _sample_idx=Mat(),
CvSVMParams _params=CvSVMParams() );
virtual bool train( const Mat& _train_data, const Mat& _responses,
const Mat& _var_idx=Mat(), const Mat& _sample_idx=Mat(),
CvSVMParams _params=CvSVMParams() );
virtual bool train_auto( const Mat& _train_data, const Mat& _responses,
const Mat& _var_idx, const Mat& _sample_idx, CvSVMParams _params,
int k_fold = 10,
CvParamGrid C_grid = get_default_grid(CvSVM::C),
CvParamGrid gamma_grid = get_default_grid(CvSVM::GAMMA),
CvParamGrid p_grid = get_default_grid(CvSVM::P),
CvParamGrid nu_grid = get_default_grid(CvSVM::NU),
CvParamGrid coef_grid = get_default_grid(CvSVM::COEF),
CvParamGrid degree_grid = get_default_grid(CvSVM::DEGREE) );
virtual float predict( const Mat& _sample ) const;
virtual int get_support_vector_count() const;
virtual const float* get_support_vector(int i) const;
virtual CvSVMParams get_params() const { return params; };
virtual void clear();
static CvParamGrid get_default_grid( int param_id );
virtual void save( const char* filename, const char* name=0 );
virtual void load( const char* filename, const char* name=0 );
virtual void write( CvFileStorage* storage, const char* name );
virtual void read( CvFileStorage* storage, CvFileNode* node );
int get_var_count() const { return var_idx ? var_idx->cols : var_all; }
protected:
...
};
.. index:: CvSVMParams
.. _CvSVMParams:
CvSVMParams
-----------
.. c:type:: CvSVMParams
SVM training parameters ::
struct CvSVMParams
{
CvSVMParams();
CvSVMParams( int _svm_type, int _kernel_type,
double _degree, double _gamma, double _coef0,
double _C, double _nu, double _p,
const CvMat* _class_weights, CvTermCriteria _term_crit );
int svm_type;
int kernel_type;
double degree; // for poly
double gamma; // for poly/rbf/sigmoid
double coef0; // for poly/sigmoid
double C; // for CV_SVM_C_SVC, CV_SVM_EPS_SVR and CV_SVM_NU_SVR
double nu; // for CV_SVM_NU_SVC, CV_SVM_ONE_CLASS, and CV_SVM_NU_SVR
double p; // for CV_SVM_EPS_SVR
CvMat* class_weights; // for CV_SVM_C_SVC
CvTermCriteria term_crit; // termination criteria
};
The structure must be initialized and passed to the training method of
:ref:`CvSVM` .
.. index:: CvSVM::train
.. _CvSVM::train:
CvSVM::train
------------
.. ocv:function:: bool CvSVM::train( const Mat& _train_data, const Mat& _responses, const Mat& _var_idx=Mat(), const Mat& _sample_idx=Mat(), CvSVMParams _params=CvSVMParams() )
Trains SVM.
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.
* 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
:ref:`CvSVMParams` structure.
.. index:: CvSVM::train_auto
.. _CvSVM::train_auto:
CvSVM::train_auto
-----------------
.. ocv:function:: train_auto( const Mat& _train_data, const Mat& _responses, const Mat& _var_idx, const Mat& _sample_idx, CvSVMParams params, int k_fold = 10, CvParamGrid C_grid = get_default_grid(CvSVM::C), CvParamGrid gamma_grid = get_default_grid(CvSVM::GAMMA), CvParamGrid p_grid = get_default_grid(CvSVM::P), CvParamGrid nu_grid = get_default_grid(CvSVM::NU), CvParamGrid coef_grid = get_default_grid(CvSVM::COEF), CvParamGrid degree_grid = get_default_grid(CvSVM::DEGREE) )
Trains SVM with optimal parameters.
:param k_fold: Cross-validation parameter. The training set is divided into ``k_fold`` subsets. One subset is used to train the model, the others form the test set. So, the SVM algorithm is executed ``k_fold`` times.
The method trains the SVM model automatically by choosing the optimal
parameters ``C`` , ``gamma`` , ``p`` , ``nu`` , ``coef0`` , ``degree`` from
:ref:`CvSVMParams`. Parameters are considered optimal
when the cross-validation estimate of the test set error
is minimal. The parameters are iterated by a logarithmic grid, for
example, the parameter ``gamma`` takes the values in the set
(
:math:`min`,
:math:`min*step`,
:math:`min*{step}^2` , ...
:math:`min*{step}^n` )
where
:math:`min` is ``gamma_grid.min_val`` ,
:math:`step` is ``gamma_grid.step`` , and
:math:`n` is the maximal index such that
.. math::
\texttt{gamma\_grid.min\_val} * \texttt{gamma\_grid.step} ^n < \texttt{gamma\_grid.max\_val}
So ``step`` must always be greater than 1.
If there is no need to optimize a parameter, the corresponding grid step should be set to any value less 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 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 parameters specified in ``params`` is executed.
.. index:: CvSVM::get_default_grid
.. _CvSVM::get_default_grid:
CvSVM::get_default_grid
-----------------------
.. ocv:function:: CvParamGrid CvSVM::get_default_grid( int param_id )
Generates a grid for SVM parameters.
:param param_id: SVN parameters IDs that must be one of the following:
* **CvSVM::C**
* **CvSVM::GAMMA**
* **CvSVM::P**
* **CvSVM::NU**
* **CvSVM::COEF**
* **CvSVM::DEGREE**
The grid will be 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 ``CvSVM::train_auto`` .
.. index:: CvSVM::get_params
.. _CvSVM::get_params:
CvSVM::get_params
-----------------
.. ocv:function:: CvSVMParams CvSVM::get_params() const
Returns the current SVM parameters.
This function may be used to get the optimal parameters obtained while automatically training ``CvSVM::train_auto`` .
.. index:: CvSVM::get_support_vector*
.. _CvSVM::get_support_vector*:
CvSVM::get_support_vector*
--------------------------
.. ocv:function:: int CvSVM::get_support_vector_count() const
.. ocv:function:: const float* CvSVM::get_support_vector(int i) const
Retrieves a number of support vectors and the particular vector.
The methods can be used to retrieve a set of support vectors.