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233 lines
9.5 KiB
ReStructuredText
233 lines
9.5 KiB
ReStructuredText
Support Vector Machines
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=======================
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.. highlight:: cpp
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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.
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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).
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There are a lot of good references on SVM. Here are only a few ones to start with.
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*
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**[Burges98] C. Burges. "A tutorial on support vector machines for pattern recognition", Knowledge Discovery and Data Mining 2(2), 1998.**
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(available online at
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http://citeseer.ist.psu.edu/burges98tutorial.html
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).
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*
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**LIBSVM - A Library for Support Vector Machines. By Chih-Chung Chang and Chih-Jen Lin**
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(
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http://www.csie.ntu.edu.tw/~cjlin/libsvm/
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)
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.. index:: CvSVM
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.. _CvSVM:
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CvSVM
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-----
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.. c:type:: CvSVM
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Support Vector Machines. ::
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class CvSVM : public CvStatModel
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{
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public:
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// SVM type
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enum { C_SVC=100, NU_SVC=101, ONE_CLASS=102, EPS_SVR=103, NU_SVR=104 };
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// SVM kernel type
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enum { LINEAR=0, POLY=1, RBF=2, SIGMOID=3 };
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// SVM params type
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enum { C=0, GAMMA=1, P=2, NU=3, COEF=4, DEGREE=5 };
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CvSVM();
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virtual ~CvSVM();
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CvSVM( const CvMat* _train_data, const CvMat* _responses,
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const CvMat* _var_idx=0, const CvMat* _sample_idx=0,
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CvSVMParams _params=CvSVMParams() );
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virtual bool train( const CvMat* _train_data, const CvMat* _responses,
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const CvMat* _var_idx=0, const CvMat* _sample_idx=0,
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CvSVMParams _params=CvSVMParams() );
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virtual bool train_auto( const CvMat* _train_data, const CvMat* _responses,
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const CvMat* _var_idx, const CvMat* _sample_idx, CvSVMParams _params,
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int k_fold = 10,
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CvParamGrid C_grid = get_default_grid(CvSVM::C),
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CvParamGrid gamma_grid = get_default_grid(CvSVM::GAMMA),
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CvParamGrid p_grid = get_default_grid(CvSVM::P),
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CvParamGrid nu_grid = get_default_grid(CvSVM::NU),
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CvParamGrid coef_grid = get_default_grid(CvSVM::COEF),
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CvParamGrid degree_grid = get_default_grid(CvSVM::DEGREE) );
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virtual float predict( const CvMat* _sample ) const;
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virtual int get_support_vector_count() const;
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virtual const float* get_support_vector(int i) const;
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virtual CvSVMParams get_params() const { return params; };
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virtual void clear();
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static CvParamGrid get_default_grid( int param_id );
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virtual void save( const char* filename, const char* name=0 );
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virtual void load( const char* filename, const char* name=0 );
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virtual void write( CvFileStorage* storage, const char* name );
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virtual void read( CvFileStorage* storage, CvFileNode* node );
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int get_var_count() const { return var_idx ? var_idx->cols : var_all; }
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protected:
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...
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};
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.. index:: CvSVMParams
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.. _CvSVMParams:
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CvSVMParams
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-----------
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.. c:type:: CvSVMParams
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SVM training parameters. ::
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struct CvSVMParams
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{
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CvSVMParams();
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CvSVMParams( int _svm_type, int _kernel_type,
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double _degree, double _gamma, double _coef0,
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double _C, double _nu, double _p,
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CvMat* _class_weights, CvTermCriteria _term_crit );
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int svm_type;
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int kernel_type;
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double degree; // for poly
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double gamma; // for poly/rbf/sigmoid
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double coef0; // for poly/sigmoid
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double C; // for CV_SVM_C_SVC, CV_SVM_EPS_SVR and CV_SVM_NU_SVR
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double nu; // for CV_SVM_NU_SVC, CV_SVM_ONE_CLASS, and CV_SVM_NU_SVR
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double p; // for CV_SVM_EPS_SVR
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CvMat* class_weights; // for CV_SVM_C_SVC
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CvTermCriteria term_crit; // termination criteria
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};
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The structure must be initialized and passed to the training method of
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:ref:`CvSVM` .
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.. index:: CvSVM::train
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.. _CvSVM::train:
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CvSVM::train
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------------
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.. c:function:: bool CvSVM::train( const CvMat* _train_data, const CvMat* _responses, const CvMat* _var_idx=0, const CvMat* _sample_idx=0, CvSVMParams _params=CvSVMParams() )
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Trains SVM.
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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.
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All the other parameters are gathered in
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:ref:`CvSVMParams` structure.
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.. index:: CvSVM::train_auto
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.. _CvSVM::train_auto:
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CvSVM::train_auto
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-----------------
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.. c:function:: train_auto( const CvMat* _train_data, const CvMat* _responses, const CvMat* _var_idx, const CvMat* _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) )
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Trains SVM with optimal parameters.
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: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.
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The method trains the SVM model automatically by choosing the optimal
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parameters ``C``,``gamma``,``p``,``nu``,``coef0``,``degree`` from
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:ref:`CvSVMParams` . By optimal
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one means that the cross-validation estimate of the test set error
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is minimal. The parameters are iterated by a logarithmic grid, for
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example, the parameter ``gamma`` takes the values in the set
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(
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:math:`min`,:math:`min*step`,:math:`min*{step}^2` , ...
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:math:`min*{step}^n` )
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where
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:math:`min` is ``gamma_grid.min_val``,:math:`step` is ``gamma_grid.step`` , and
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:math:`n` is the maximal index such, that
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.. math::
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\texttt{gamma\_grid.min\_val} * \texttt{gamma\_grid.step} ^n < \texttt{gamma\_grid.max\_val}
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So ``step`` must always be greater than 1.
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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`` .
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And, finally, if the optimization in some parameter is required, but
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there is no idea of the corresponding grid, one may call the function ``CvSVM::get_default_grid`` . In
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order to generate a grid, say, for ``gamma`` , call ``CvSVM::get_default_grid(CvSVM::GAMMA)`` .
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This function works for the case of classification
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( ``params.svm_type=CvSVM::C_SVC`` or ``params.svm_type=CvSVM::NU_SVC`` )
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as well as for the regression
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( ``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.
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.. index:: CvSVM::get_default_grid
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.. _CvSVM::get_default_grid:
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CvSVM::get_default_grid
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-----------------------
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.. c:function:: CvParamGrid CvSVM::get_default_grid( int param_id )
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Generates a grid for the SVM parameters.
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:param param_id: Must be one of the following:
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* **CvSVM::C**
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* **CvSVM::GAMMA**
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* **CvSVM::P**
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* **CvSVM::NU**
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* **CvSVM::COEF**
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* **CvSVM::DEGREE**
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The grid will be generated for the parameter with this ID.
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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`` .
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.. index:: CvSVM::get_params
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.. _CvSVM::get_params:
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CvSVM::get_params
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-----------------
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.. c:function:: CvSVMParams CvSVM::get_params() const
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Returns the current SVM parameters.
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This function may be used to get the optimal parameters that were obtained while automatically training ``CvSVM::train_auto`` .
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.. index:: CvSVM::get_support_vector*
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.. _CvSVM::get_support_vector*:
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CvSVM::get_support_vector*
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--------------------------
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.. c:function:: int CvSVM::get_support_vector_count() const
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.. c:function:: const float* CvSVM::get_support_vector(int i) const
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Retrieves the number of support vectors and the particular vector.
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The methods can be used to retrieve the set of support vectors.
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