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239 lines
9.5 KiB
239 lines
9.5 KiB
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 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. |
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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). |
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There are a lot of good references on SVM. You may consider starting with the following: |
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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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Chih-Chung Chang and Chih-Jen Lin. *LIBSVM - A Library for Support Vector Machines* |
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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: |
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* Only the ``CV_ROW_SAMPLE`` data layout is supported. |
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* Input variables are all ordered. |
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* 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`` ). |
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* Missing measurements are not supported. |
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All the other parameters are gathered in the |
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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 is used to train the model, the others form 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`. Parameters are considered optimal |
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when 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`, |
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:math:`min*step`, |
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: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`` , |
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: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 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`` . |
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And, finally, if the optimization in a parameter is required but |
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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)`` . |
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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 parameters specified in ``params`` 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 SVM parameters. |
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:param param_id: SVN parameters IDs that 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 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 a number of support vectors and the particular vector. |
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The methods can be used to retrieve a set of support vectors. |
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