ImageProcess/Archive/ios/opencv2.framework/Versions/A/Headers/ml.hpp

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#ifndef OPENCV_ML_HPP
#define OPENCV_ML_HPP

#ifdef __cplusplus
#  include "opencv2/core.hpp"
#endif

#ifdef __cplusplus

#include <float.h>
#include <map>
#include <iostream>

/**
  @defgroup ml Machine Learning

  The Machine Learning Library (MLL) is a set of classes and functions for statistical
  classification, regression, and clustering of data.

  Most of the classification and regression algorithms are implemented as C++ classes. As the
  algorithms have different sets of features (like an ability to handle missing measurements or
  categorical input variables), there is a little common ground between the classes. This common
  ground is defined by the class cv::ml::StatModel that all the other ML classes are derived from.

  See detailed overview here: @ref ml_intro.
 */

namespace cv
{

namespace ml
{

//! @addtogroup ml
//! @{

/** @brief Variable types */
enum VariableTypes
{
    VAR_NUMERICAL    =0, //!< same as VAR_ORDERED
    VAR_ORDERED      =0, //!< ordered variables
    VAR_CATEGORICAL  =1  //!< categorical variables
};

/** @brief %Error types */
enum ErrorTypes
{
    TEST_ERROR = 0,
    TRAIN_ERROR = 1
};

/** @brief Sample types */
enum SampleTypes
{
    ROW_SAMPLE = 0, //!< each training sample is a row of samples
    COL_SAMPLE = 1  //!< each training sample occupies a column of samples
};

/** @brief 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.
 */
class CV_EXPORTS_W ParamGrid
{
public:
    /** @brief Default constructor */
    ParamGrid();
    /** @brief Constructor with parameters */
    ParamGrid(double _minVal, double _maxVal, double _logStep);

    CV_PROP_RW double minVal; //!< Minimum value of the statmodel parameter. Default value is 0.
    CV_PROP_RW double maxVal; //!< Maximum value of the statmodel parameter. Default value is 0.
    /** @brief Logarithmic step for iterating the statmodel parameter.

    The grid determines the following iteration sequence of the statmodel parameter values:
    \f[(minVal, minVal*step, minVal*{step}^2, \dots,  minVal*{logStep}^n),\f]
    where \f$n\f$ is the maximal index satisfying
    \f[\texttt{minVal} * \texttt{logStep} ^n <  \texttt{maxVal}\f]
    The grid is logarithmic, so logStep must always be greater than 1. Default value is 1.
    */
    CV_PROP_RW double logStep;

    /** @brief Creates a ParamGrid Ptr that can be given to the %SVM::trainAuto method

    @param minVal minimum value of the parameter grid
    @param maxVal maximum value of the parameter grid
    @param logstep Logarithmic step for iterating the statmodel parameter
    */
    CV_WRAP static Ptr<ParamGrid> create(double minVal=0., double maxVal=0., double logstep=1.);
};

/** @brief Class encapsulating training data.

Please note that the class only specifies the interface of training data, but not implementation.
All the statistical model classes in _ml_ module accepts Ptr\<TrainData\> as parameter. In other
words, you can create your own class derived from TrainData and pass smart pointer to the instance
of this class into StatModel::train.

@sa @ref ml_intro_data
 */
class CV_EXPORTS_W TrainData
{
public:
    static inline float missingValue() { return FLT_MAX; }
    virtual ~TrainData();

    CV_WRAP virtual int getLayout() const = 0;
    CV_WRAP virtual int getNTrainSamples() const = 0;
    CV_WRAP virtual int getNTestSamples() const = 0;
    CV_WRAP virtual int getNSamples() const = 0;
    CV_WRAP virtual int getNVars() const = 0;
    CV_WRAP virtual int getNAllVars() const = 0;

    CV_WRAP virtual void getSample(InputArray varIdx, int sidx, float* buf) const = 0;
    CV_WRAP virtual Mat getSamples() const = 0;
    CV_WRAP virtual Mat getMissing() const = 0;

    /** @brief Returns matrix of train samples

    @param layout The requested layout. If it's different from the initial one, the matrix is
        transposed. See ml::SampleTypes.
    @param compressSamples if true, the function returns only the training samples (specified by
        sampleIdx)
    @param compressVars if true, the function returns the shorter training samples, containing only
        the active variables.

    In current implementation the function tries to avoid physical data copying and returns the
    matrix stored inside TrainData (unless the transposition or compression is needed).
     */
    CV_WRAP virtual Mat getTrainSamples(int layout=ROW_SAMPLE,
                                bool compressSamples=true,
                                bool compressVars=true) const = 0;

    /** @brief Returns the vector of responses

    The function returns ordered or the original categorical responses. Usually it's used in
    regression algorithms.
     */
    CV_WRAP virtual Mat getTrainResponses() const = 0;

    /** @brief Returns the vector of normalized categorical responses

    The function returns vector of responses. Each response is integer from `0` to `<number of
    classes>-1`. The actual label value can be retrieved then from the class label vector, see
    TrainData::getClassLabels.
     */
    CV_WRAP virtual Mat getTrainNormCatResponses() const = 0;
    CV_WRAP virtual Mat getTestResponses() const = 0;
    CV_WRAP virtual Mat getTestNormCatResponses() const = 0;
    CV_WRAP virtual Mat getResponses() const = 0;
    CV_WRAP virtual Mat getNormCatResponses() const = 0;
    CV_WRAP virtual Mat getSampleWeights() const = 0;
    CV_WRAP virtual Mat getTrainSampleWeights() const = 0;
    CV_WRAP virtual Mat getTestSampleWeights() const = 0;
    CV_WRAP virtual Mat getVarIdx() const = 0;
    CV_WRAP virtual Mat getVarType() const = 0;
    CV_WRAP virtual Mat getVarSymbolFlags() const = 0;
    CV_WRAP virtual int getResponseType() const = 0;
    CV_WRAP virtual Mat getTrainSampleIdx() const = 0;
    CV_WRAP virtual Mat getTestSampleIdx() const = 0;
    CV_WRAP virtual void getValues(int vi, InputArray sidx, float* values) const = 0;
    virtual void getNormCatValues(int vi, InputArray sidx, int* values) const = 0;
    CV_WRAP virtual Mat getDefaultSubstValues() const = 0;

    CV_WRAP virtual int getCatCount(int vi) const = 0;

    /** @brief Returns the vector of class labels

    The function returns vector of unique labels occurred in the responses.
     */
    CV_WRAP virtual Mat getClassLabels() const = 0;

    CV_WRAP virtual Mat getCatOfs() const = 0;
    CV_WRAP virtual Mat getCatMap() const = 0;

    /** @brief Splits the training data into the training and test parts
    @sa TrainData::setTrainTestSplitRatio
     */
    CV_WRAP virtual void setTrainTestSplit(int count, bool shuffle=true) = 0;

    /** @brief Splits the training data into the training and test parts

    The function selects a subset of specified relative size and then returns it as the training
    set. If the function is not called, all the data is used for training. Please, note that for
    each of TrainData::getTrain\* there is corresponding TrainData::getTest\*, so that the test
    subset can be retrieved and processed as well.
    @sa TrainData::setTrainTestSplit
     */
    CV_WRAP virtual void setTrainTestSplitRatio(double ratio, bool shuffle=true) = 0;
    CV_WRAP virtual void shuffleTrainTest() = 0;

    /** @brief Returns matrix of test samples */
    CV_WRAP virtual Mat getTestSamples() const = 0;

    /** @brief Returns vector of symbolic names captured in loadFromCSV() */
    CV_WRAP virtual void getNames(std::vector<String>& names) const = 0;

    /** @brief Extract from 1D vector elements specified by passed indexes.
    @param vec input vector (supported types: CV_32S, CV_32F, CV_64F)
    @param idx 1D index vector
     */
    static CV_WRAP Mat getSubVector(const Mat& vec, const Mat& idx);

    /** @brief Extract from matrix rows/cols specified by passed indexes.
    @param matrix input matrix (supported types: CV_32S, CV_32F, CV_64F)
    @param idx 1D index vector
    @param layout specifies to extract rows (cv::ml::ROW_SAMPLES) or to extract columns (cv::ml::COL_SAMPLES)
     */
    static CV_WRAP Mat getSubMatrix(const Mat& matrix, const Mat& idx, int layout);

    /** @brief Reads the dataset from a .csv file and returns the ready-to-use training data.

    @param filename The input file name
    @param headerLineCount The number of lines in the beginning to skip; besides the header, the
        function also skips empty lines and lines staring with `#`
    @param responseStartIdx Index of the first output variable. If -1, the function considers the
        last variable as the response
    @param responseEndIdx Index of the last output variable + 1. If -1, then there is single
        response variable at responseStartIdx.
    @param varTypeSpec The optional text string that specifies the variables' types. It has the
        format `ord[n1-n2,n3,n4-n5,...]cat[n6,n7-n8,...]`. That is, variables from `n1 to n2`
        (inclusive range), `n3`, `n4 to n5` ... are considered ordered and `n6`, `n7 to n8` ... are
        considered as categorical. The range `[n1..n2] + [n3] + [n4..n5] + ... + [n6] + [n7..n8]`
        should cover all the variables. If varTypeSpec is not specified, then algorithm uses the
        following rules:
        - all input variables are considered ordered by default. If some column contains has non-
          numerical values, e.g. 'apple', 'pear', 'apple', 'apple', 'mango', the corresponding
          variable is considered categorical.
        - if there are several output variables, they are all considered as ordered. Error is
          reported when non-numerical values are used.
        - if there is a single output variable, then if its values are non-numerical or are all
          integers, then it's considered categorical. Otherwise, it's considered ordered.
    @param delimiter The character used to separate values in each line.
    @param missch The character used to specify missing measurements. It should not be a digit.
        Although it's a non-numerical value, it surely does not affect the decision of whether the
        variable ordered or categorical.
    @note If the dataset only contains input variables and no responses, use responseStartIdx = -2
        and responseEndIdx = 0. The output variables vector will just contain zeros.
     */
    static Ptr<TrainData> loadFromCSV(const String& filename,
                                      int headerLineCount,
                                      int responseStartIdx=-1,
                                      int responseEndIdx=-1,
                                      const String& varTypeSpec=String(),
                                      char delimiter=',',
                                      char missch='?');

    /** @brief Creates training data from in-memory arrays.

    @param samples matrix of samples. It should have CV_32F type.
    @param layout see ml::SampleTypes.
    @param responses matrix of responses. If the responses are scalar, they should be stored as a
        single row or as a single column. The matrix should have type CV_32F or CV_32S (in the
        former case the responses are considered as ordered by default; in the latter case - as
        categorical)
    @param varIdx vector specifying which variables to use for training. It can be an integer vector
        (CV_32S) containing 0-based variable indices or byte vector (CV_8U) containing a mask of
        active variables.
    @param sampleIdx vector specifying which samples to use for training. It can be an integer
        vector (CV_32S) containing 0-based sample indices or byte vector (CV_8U) containing a mask
        of training samples.
    @param sampleWeights optional vector with weights for each sample. It should have CV_32F type.
    @param varType optional vector of type CV_8U and size `<number_of_variables_in_samples> +
        <number_of_variables_in_responses>`, containing types of each input and output variable. See
        ml::VariableTypes.
     */
    CV_WRAP static Ptr<TrainData> create(InputArray samples, int layout, InputArray responses,
                                 InputArray varIdx=noArray(), InputArray sampleIdx=noArray(),
                                 InputArray sampleWeights=noArray(), InputArray varType=noArray());
};

/** @brief Base class for statistical models in OpenCV ML.
 */
class CV_EXPORTS_W StatModel : public Algorithm
{
public:
    /** Predict options */
    enum Flags {
        UPDATE_MODEL = 1,
        RAW_OUTPUT=1, //!< makes the method return the raw results (the sum), not the class label
        COMPRESSED_INPUT=2,
        PREPROCESSED_INPUT=4
    };

    /** @brief Returns the number of variables in training samples */
    CV_WRAP virtual int getVarCount() const = 0;

    CV_WRAP virtual bool empty() const CV_OVERRIDE;

    /** @brief Returns true if the model is trained */
    CV_WRAP virtual bool isTrained() const = 0;
    /** @brief Returns true if the model is classifier */
    CV_WRAP virtual bool isClassifier() const = 0;

    /** @brief Trains the statistical model

    @param trainData training data that can be loaded from file using TrainData::loadFromCSV or
        created with TrainData::create.
    @param flags optional flags, depending on the model. Some of the models can be updated with the
        new training samples, not completely overwritten (such as NormalBayesClassifier or ANN_MLP).
     */
    CV_WRAP virtual bool train( const Ptr<TrainData>& trainData, int flags=0 );

    /** @brief Trains the statistical model

    @param samples training samples
    @param layout See ml::SampleTypes.
    @param responses vector of responses associated with the training samples.
    */
    CV_WRAP virtual bool train( InputArray samples, int layout, InputArray responses );

    /** @brief Computes error on the training or test dataset

    @param data the training data
    @param test if true, the error is computed over the test subset of the data, otherwise it's
        computed over the training subset of the data. Please note that if you loaded a completely
        different dataset to evaluate already trained classifier, you will probably want not to set
        the test subset at all with TrainData::setTrainTestSplitRatio and specify test=false, so
        that the error is computed for the whole new set. Yes, this sounds a bit confusing.
    @param resp the optional output responses.

    The method uses StatModel::predict to compute the error. For regression models the error is
    computed as RMS, for classifiers - as a percent of missclassified samples (0%-100%).
     */
    CV_WRAP virtual float calcError( const Ptr<TrainData>& data, bool test, OutputArray resp ) const;

    /** @brief Predicts response(s) for the provided sample(s)

    @param samples The input samples, floating-point matrix
    @param results The optional output matrix of results.
    @param flags The optional flags, model-dependent. See cv::ml::StatModel::Flags.
     */
    CV_WRAP virtual float predict( InputArray samples, OutputArray results=noArray(), int flags=0 ) const = 0;

    /** @brief Create and train model with default parameters

    The class must implement static `create()` method with no parameters or with all default parameter values
    */
    template<typename _Tp> static Ptr<_Tp> train(const Ptr<TrainData>& data, int flags=0)
    {
        Ptr<_Tp> model = _Tp::create();
        return !model.empty() && model->train(data, flags) ? model : Ptr<_Tp>();
    }
};

/****************************************************************************************\
*                                 Normal Bayes Classifier                                *
\****************************************************************************************/

/** @brief Bayes classifier for normally distributed data.

@sa @ref ml_intro_bayes
 */
class CV_EXPORTS_W NormalBayesClassifier : public StatModel
{
public:
    /** @brief Predicts the response for sample(s).

    The method estimates the most probable classes for input vectors. Input vectors (one or more)
    are stored as rows of the matrix inputs. In case of multiple input vectors, there should be one
    output vector outputs. The predicted class for a single input vector is returned by the method.
    The vector outputProbs contains the output probabilities corresponding to each element of
    result.
     */
    CV_WRAP virtual float predictProb( InputArray inputs, OutputArray outputs,
                               OutputArray outputProbs, int flags=0 ) const = 0;

    /** Creates empty model
    Use StatModel::train to train the model after creation. */
    CV_WRAP static Ptr<NormalBayesClassifier> create();

    /** @brief Loads and creates a serialized NormalBayesClassifier from a file
     *
     * Use NormalBayesClassifier::save to serialize and store an NormalBayesClassifier to disk.
     * Load the NormalBayesClassifier from this file again, by calling this function with the path to the file.
     * Optionally specify the node for the file containing the classifier
     *
     * @param filepath path to serialized NormalBayesClassifier
     * @param nodeName name of node containing the classifier
     */
    CV_WRAP static Ptr<NormalBayesClassifier> load(const String& filepath , const String& nodeName = String());
};

/****************************************************************************************\
*                          K-Nearest Neighbour Classifier                                *
\****************************************************************************************/

/** @brief The class implements K-Nearest Neighbors model

@sa @ref ml_intro_knn
 */
class CV_EXPORTS_W KNearest : public StatModel
{
public:

    /** Default number of neighbors to use in predict method. */
    /** @see setDefaultK */
    CV_WRAP virtual int getDefaultK() const = 0;
    /** @copybrief getDefaultK @see getDefaultK */
    CV_WRAP virtual void setDefaultK(int val) = 0;

    /** Whether classification or regression model should be trained. */
    /** @see setIsClassifier */
    CV_WRAP virtual bool getIsClassifier() const = 0;
    /** @copybrief getIsClassifier @see getIsClassifier */
    CV_WRAP virtual void setIsClassifier(bool val) = 0;

    /** Parameter for KDTree implementation. */
    /** @see setEmax */
    CV_WRAP virtual int getEmax() const = 0;
    /** @copybrief getEmax @see getEmax */
    CV_WRAP virtual void setEmax(int val) = 0;

    /** %Algorithm type, one of KNearest::Types. */
    /** @see setAlgorithmType */
    CV_WRAP virtual int getAlgorithmType() const = 0;
    /** @copybrief getAlgorithmType @see getAlgorithmType */
    CV_WRAP virtual void setAlgorithmType(int val) = 0;

    /** @brief Finds the neighbors and predicts responses for input vectors.

    @param samples Input samples stored by rows. It is a single-precision floating-point matrix of
        `<number_of_samples> * k` size.
    @param k Number of used nearest neighbors. Should be greater than 1.
    @param results Vector with results of prediction (regression or classification) for each input
        sample. It is a single-precision floating-point vector with `<number_of_samples>` elements.
    @param neighborResponses Optional output values for corresponding neighbors. It is a single-
        precision floating-point matrix of `<number_of_samples> * k` size.
    @param dist Optional output distances from the input vectors to the corresponding neighbors. It
        is a single-precision floating-point matrix of `<number_of_samples> * k` size.

    For each input vector (a row of the matrix samples), the method finds the k nearest neighbors.
    In case of regression, the predicted result is a mean value of the particular vector's neighbor
    responses. In case of classification, the class is determined by voting.

    For each input vector, the neighbors are sorted by their distances to the vector.

    In case of C++ interface you can use output pointers to empty matrices and the function will
    allocate memory itself.

    If only a single input vector is passed, all output matrices are optional and the predicted
    value is returned by the method.

    The function is parallelized with the TBB library.
     */
    CV_WRAP virtual float findNearest( InputArray samples, int k,
                               OutputArray results,
                               OutputArray neighborResponses=noArray(),
                               OutputArray dist=noArray() ) const = 0;

    /** @brief Implementations of KNearest algorithm
       */
    enum Types
    {
        BRUTE_FORCE=1,
        KDTREE=2
    };

    /** @brief Creates the empty model

    The static method creates empty %KNearest classifier. It should be then trained using StatModel::train method.
     */
    CV_WRAP static Ptr<KNearest> create();
    /** @brief Loads and creates a serialized knearest from a file
     *
     * Use KNearest::save to serialize and store an KNearest to disk.
     * Load the KNearest from this file again, by calling this function with the path to the file.
     *
     * @param filepath path to serialized KNearest
     */
    CV_WRAP static Ptr<KNearest> load(const String& filepath);
};

/****************************************************************************************\
*                                   Support Vector Machines                              *
\****************************************************************************************/

/** @brief Support Vector Machines.

@sa @ref ml_intro_svm
 */
class CV_EXPORTS_W SVM : public StatModel
{
public:

    class CV_EXPORTS Kernel : public Algorithm
    {
    public:
        virtual int getType() const = 0;
        virtual void calc( int vcount, int n, const float* vecs, const float* another, float* results ) = 0;
    };

    /** Type of a %SVM formulation.
    See SVM::Types. Default value is SVM::C_SVC. */
    /** @see setType */
    CV_WRAP virtual int getType() const = 0;
    /** @copybrief getType @see getType */
    CV_WRAP virtual void setType(int val) = 0;

    /** Parameter \f$\gamma\f$ of a kernel function.
    For SVM::POLY, SVM::RBF, SVM::SIGMOID or SVM::CHI2. Default value is 1. */
    /** @see setGamma */
    CV_WRAP virtual double getGamma() const = 0;
    /** @copybrief getGamma @see getGamma */
    CV_WRAP virtual void setGamma(double val) = 0;

    /** Parameter _coef0_ of a kernel function.
    For SVM::POLY or SVM::SIGMOID. Default value is 0.*/
    /** @see setCoef0 */
    CV_WRAP virtual double getCoef0() const = 0;
    /** @copybrief getCoef0 @see getCoef0 */
    CV_WRAP virtual void setCoef0(double val) = 0;

    /** Parameter _degree_ of a kernel function.
    For SVM::POLY. Default value is 0. */
    /** @see setDegree */
    CV_WRAP virtual double getDegree() const = 0;
    /** @copybrief getDegree @see getDegree */
    CV_WRAP virtual void setDegree(double val) = 0;

    /** Parameter _C_ of a %SVM optimization problem.
    For SVM::C_SVC, SVM::EPS_SVR or SVM::NU_SVR. Default value is 0. */
    /** @see setC */
    CV_WRAP virtual double getC() const = 0;
    /** @copybrief getC @see getC */
    CV_WRAP virtual void setC(double val) = 0;

    /** Parameter \f$\nu\f$ of a %SVM optimization problem.
    For SVM::NU_SVC, SVM::ONE_CLASS or SVM::NU_SVR. Default value is 0. */
    /** @see setNu */
    CV_WRAP virtual double getNu() const = 0;
    /** @copybrief getNu @see getNu */
    CV_WRAP virtual void setNu(double val) = 0;

    /** Parameter \f$\epsilon\f$ of a %SVM optimization problem.
    For SVM::EPS_SVR. Default value is 0. */
    /** @see setP */
    CV_WRAP virtual double getP() const = 0;
    /** @copybrief getP @see getP */
    CV_WRAP virtual void setP(double val) = 0;

    /** Optional weights in the SVM::C_SVC problem, assigned to particular classes.
    They are multiplied by _C_ so the parameter _C_ of class _i_ becomes `classWeights(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. Default value is
    empty Mat. */
    /** @see setClassWeights */
    CV_WRAP virtual cv::Mat getClassWeights() const = 0;
    /** @copybrief getClassWeights @see getClassWeights */
    CV_WRAP virtual void setClassWeights(const cv::Mat &val) = 0;

    /** 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. Default value is
    `TermCriteria( TermCriteria::MAX_ITER + TermCriteria::EPS, 1000, FLT_EPSILON )`; */
    /** @see setTermCriteria */
    CV_WRAP virtual cv::TermCriteria getTermCriteria() const = 0;
    /** @copybrief getTermCriteria @see getTermCriteria */
    CV_WRAP virtual void setTermCriteria(const cv::TermCriteria &val) = 0;

    /** Type of a %SVM kernel.
    See SVM::KernelTypes. Default value is SVM::RBF. */
    CV_WRAP virtual int getKernelType() const = 0;

    /** Initialize with one of predefined kernels.
    See SVM::KernelTypes. */
    CV_WRAP virtual void setKernel(int kernelType) = 0;

    /** Initialize with custom kernel.
    See SVM::Kernel class for implementation details */
    virtual void setCustomKernel(const Ptr<Kernel> &_kernel) = 0;

    //! %SVM type
    enum Types {
        /** C-Support Vector Classification. n-class classification (n \f$\geq\f$ 2), allows
        imperfect separation of classes with penalty multiplier C for outliers. */
        C_SVC=100,
        /** \f$\nu\f$-Support Vector Classification. n-class classification with possible
        imperfect separation. Parameter \f$\nu\f$ (in the range 0..1, the larger the value, the smoother
        the decision boundary) is used instead of C. */
        NU_SVC=101,
        /** 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. */
        ONE_CLASS=102,
        /** \f$\epsilon\f$-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. */
        EPS_SVR=103,
        /** \f$\nu\f$-Support Vector Regression. \f$\nu\f$ is used instead of p.
        See @cite LibSVM for details. */
        NU_SVR=104
    };

    /** @brief %SVM kernel type

    A comparison of different kernels on the following 2D test case with four classes. Four
    SVM::C_SVC SVMs have been trained (one against rest) with auto_train. Evaluation on three
    different kernels (SVM::CHI2, SVM::INTER, SVM::RBF). The color depicts the class with max score.
    Bright means max-score \> 0, dark means max-score \< 0.
    ![image](pics/SVM_Comparison.png)
    */
    enum KernelTypes {
        /** Returned by SVM::getKernelType in case when custom kernel has been set */
        CUSTOM=-1,
        /** Linear kernel. No mapping is done, linear discrimination (or regression) is
        done in the original feature space. It is the fastest option. \f$K(x_i, x_j) = x_i^T x_j\f$. */
        LINEAR=0,
        /** Polynomial kernel:
        \f$K(x_i, x_j) = (\gamma x_i^T x_j + coef0)^{degree}, \gamma > 0\f$. */
        POLY=1,
        /** Radial basis function (RBF), a good choice in most cases.
        \f$K(x_i, x_j) = e^{-\gamma ||x_i - x_j||^2}, \gamma > 0\f$. */
        RBF=2,
        /** Sigmoid kernel: \f$K(x_i, x_j) = \tanh(\gamma x_i^T x_j + coef0)\f$. */
        SIGMOID=3,
        /** Exponential Chi2 kernel, similar to the RBF kernel:
        \f$K(x_i, x_j) = e^{-\gamma \chi^2(x_i,x_j)}, \chi^2(x_i,x_j) = (x_i-x_j)^2/(x_i+x_j), \gamma > 0\f$. */
        CHI2=4,
        /** Histogram intersection kernel. A fast kernel. \f$K(x_i, x_j) = min(x_i,x_j)\f$. */
        INTER=5
    };

    //! %SVM params type
    enum ParamTypes {
        C=0,
        GAMMA=1,
        P=2,
        NU=3,
        COEF=4,
        DEGREE=5
    };

    /** @brief Trains an %SVM with optimal parameters.

    @param data the training data that can be constructed using TrainData::create or
        TrainData::loadFromCSV.
    @param kFold Cross-validation parameter. The training set is divided into kFold subsets. One
        subset is used to test the model, the others form the train set. So, the %SVM algorithm is
        executed kFold times.
    @param Cgrid grid for C
    @param gammaGrid grid for gamma
    @param pGrid grid for p
    @param nuGrid grid for nu
    @param coeffGrid grid for coeff
    @param degreeGrid grid for degree
    @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. 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 `gammaGrid.step
    = 0`, `gammaGrid.minVal`, `gamma_grid.maxVal` as arbitrary numbers. In this case, the value
    `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 SVM::getDefaultGrid. To generate a grid, for example, for
    gamma, call `SVM::getDefaultGrid(SVM::GAMMA)`.

    This function works for the classification (SVM::C_SVC or SVM::NU_SVC) as well as for the
    regression (SVM::EPS_SVR or SVM::NU_SVR). If it is SVM::ONE_CLASS, no optimization is made and
    the usual %SVM with parameters specified in params is executed.
     */
    virtual bool trainAuto( const Ptr<TrainData>& data, int kFold = 10,
                    ParamGrid Cgrid = getDefaultGrid(C),
                    ParamGrid gammaGrid  = getDefaultGrid(GAMMA),
                    ParamGrid pGrid      = getDefaultGrid(P),
                    ParamGrid nuGrid     = getDefaultGrid(NU),
                    ParamGrid coeffGrid  = getDefaultGrid(COEF),
                    ParamGrid degreeGrid = getDefaultGrid(DEGREE),
                    bool balanced=false) = 0;

    /** @brief Trains an %SVM with optimal parameters

    @param samples training samples
    @param layout See ml::SampleTypes.
    @param responses vector of responses associated with the training samples.
    @param kFold Cross-validation parameter. The training set is divided into kFold subsets. One
        subset is used to test the model, the others form the train set. So, the %SVM algorithm is
    @param Cgrid grid for C
    @param gammaGrid grid for gamma
    @param pGrid grid for p
    @param nuGrid grid for nu
    @param coeffGrid grid for coeff
    @param degreeGrid grid for degree
    @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. Parameters are considered optimal when the cross-validation
    estimate of the test set error is minimal.

    This function only makes use of SVM::getDefaultGrid for parameter optimization and thus only
    offers rudimentary parameter options.

    This function works for the classification (SVM::C_SVC or SVM::NU_SVC) as well as for the
    regression (SVM::EPS_SVR or SVM::NU_SVR). If it is SVM::ONE_CLASS, no optimization is made and
    the usual %SVM with parameters specified in params is executed.
    */
    CV_WRAP virtual bool trainAuto(InputArray samples,
            int layout,
            InputArray responses,
            int kFold = 10,
            Ptr<ParamGrid> Cgrid = SVM::getDefaultGridPtr(SVM::C),
            Ptr<ParamGrid> gammaGrid  = SVM::getDefaultGridPtr(SVM::GAMMA),
            Ptr<ParamGrid> pGrid      = SVM::getDefaultGridPtr(SVM::P),
            Ptr<ParamGrid> nuGrid     = SVM::getDefaultGridPtr(SVM::NU),
            Ptr<ParamGrid> coeffGrid  = SVM::getDefaultGridPtr(SVM::COEF),
            Ptr<ParamGrid> degreeGrid = SVM::getDefaultGridPtr(SVM::DEGREE),
            bool balanced=false) = 0;

    /** @brief Retrieves all the support vectors

    The method returns all the support vectors as a floating-point matrix, where support vectors are
    stored as matrix rows.
     */
    CV_WRAP virtual Mat getSupportVectors() const = 0;

    /** @brief Retrieves all the uncompressed support vectors of a linear %SVM

    The method returns all the uncompressed support vectors of a linear %SVM that the compressed
    support vector, used for prediction, was derived from. They are returned in a floating-point
    matrix, where the support vectors are stored as matrix rows.
     */
    CV_WRAP virtual Mat getUncompressedSupportVectors() const = 0;

    /** @brief Retrieves the decision function

    @param i the index of the decision function. If the problem solved is regression, 1-class or
        2-class classification, then there will be just one decision function and the index should
        always be 0. Otherwise, in the case of N-class classification, there will be \f$N(N-1)/2\f$
        decision functions.
    @param alpha the optional output vector for weights, corresponding to different support vectors.
        In the case of linear %SVM all the alpha's will be 1's.
    @param svidx the optional output vector of indices of support vectors within the matrix of
        support vectors (which can be retrieved by SVM::getSupportVectors). In the case of linear
        %SVM each decision function consists of a single "compressed" support vector.

    The method returns rho parameter of the decision function, a scalar subtracted from the weighted
    sum of kernel responses.
     */
    CV_WRAP virtual double getDecisionFunction(int i, OutputArray alpha, OutputArray svidx) const = 0;

    /** @brief Generates a grid for %SVM parameters.

    @param param_id %SVM parameters IDs that must be one of the SVM::ParamTypes. 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 SVM::trainAuto.
     */
    static ParamGrid getDefaultGrid( int param_id );

    /** @brief Generates a grid for %SVM parameters.

    @param param_id %SVM parameters IDs that must be one of the SVM::ParamTypes. The grid is
    generated for the parameter with this ID.

    The function generates a grid pointer for the specified parameter of the %SVM algorithm.
    The grid may be passed to the function SVM::trainAuto.
     */
    CV_WRAP static Ptr<ParamGrid> getDefaultGridPtr( int param_id );

    /** Creates empty model.
    Use StatModel::train to train the model. Since %SVM has several parameters, you may want to
    find the best parameters for your problem, it can be done with SVM::trainAuto. */
    CV_WRAP static Ptr<SVM> create();

    /** @brief Loads and creates a serialized svm from a file
     *
     * Use SVM::save to serialize and store an SVM to disk.
     * Load the SVM from this file again, by calling this function with the path to the file.
     *
     * @param filepath path to serialized svm
     */
    CV_WRAP static Ptr<SVM> load(const String& filepath);
};

/****************************************************************************************\
*                              Expectation - Maximization                                *
\****************************************************************************************/

/** @brief The class implements the Expectation Maximization algorithm.

@sa @ref ml_intro_em
 */
class CV_EXPORTS_W EM : public StatModel
{
public:
    //! Type of covariation matrices
    enum Types {
        /** A scaled identity matrix \f$\mu_k * I\f$. There is the only
        parameter \f$\mu_k\f$ to be estimated for each matrix. The option may be used in special cases,
        when the constraint is relevant, or as a first step in the optimization (for example in case
        when the data is preprocessed with PCA). The results of such preliminary estimation may be
        passed again to the optimization procedure, this time with
        covMatType=EM::COV_MAT_DIAGONAL. */
        COV_MAT_SPHERICAL=0,
        /** A diagonal matrix with positive diagonal elements. The number of
        free parameters is d for each matrix. This is most commonly used option yielding good
        estimation results. */
        COV_MAT_DIAGONAL=1,
        /** A symmetric positively defined matrix. The number of free
        parameters in each matrix is about \f$d^2/2\f$. It is not recommended to use this option, unless
        there is pretty accurate initial estimation of the parameters and/or a huge number of
        training samples. */
        COV_MAT_GENERIC=2,
        COV_MAT_DEFAULT=COV_MAT_DIAGONAL
    };

    //! Default parameters
    enum {DEFAULT_NCLUSTERS=5, DEFAULT_MAX_ITERS=100};

    //! The initial step
    enum {START_E_STEP=1, START_M_STEP=2, START_AUTO_STEP=0};

    /** The number of mixture components in the Gaussian mixture model.
    Default value of the parameter is EM::DEFAULT_NCLUSTERS=5. Some of %EM implementation could
    determine the optimal number of mixtures within a specified value range, but that is not the
    case in ML yet. */
    /** @see setClustersNumber */
    CV_WRAP virtual int getClustersNumber() const = 0;
    /** @copybrief getClustersNumber @see getClustersNumber */
    CV_WRAP virtual void setClustersNumber(int val) = 0;

    /** Constraint on covariance matrices which defines type of matrices.
    See EM::Types. */
    /** @see setCovarianceMatrixType */
    CV_WRAP virtual int getCovarianceMatrixType() const = 0;
    /** @copybrief getCovarianceMatrixType @see getCovarianceMatrixType */
    CV_WRAP virtual void setCovarianceMatrixType(int val) = 0;

    /** The termination criteria of the %EM algorithm.
    The %EM algorithm can be terminated by the number of iterations termCrit.maxCount (number of
    M-steps) or when relative change of likelihood logarithm is less than termCrit.epsilon. Default
    maximum number of iterations is EM::DEFAULT_MAX_ITERS=100. */
    /** @see setTermCriteria */
    CV_WRAP virtual TermCriteria getTermCriteria() const = 0;
    /** @copybrief getTermCriteria @see getTermCriteria */
    CV_WRAP virtual void setTermCriteria(const TermCriteria &val) = 0;

    /** @brief Returns weights of the mixtures

    Returns vector with the number of elements equal to the number of mixtures.
     */
    CV_WRAP virtual Mat getWeights() const = 0;
    /** @brief Returns the cluster centers (means of the Gaussian mixture)

    Returns matrix with the number of rows equal to the number of mixtures and number of columns
    equal to the space dimensionality.
     */
    CV_WRAP virtual Mat getMeans() const = 0;
    /** @brief Returns covariation matrices

    Returns vector of covariation matrices. Number of matrices is the number of gaussian mixtures,
    each matrix is a square floating-point matrix NxN, where N is the space dimensionality.
     */
    CV_WRAP virtual void getCovs(CV_OUT std::vector<Mat>& covs) const = 0;

    /** @brief Returns posterior probabilities for the provided samples

    @param samples The input samples, floating-point matrix
    @param results The optional output \f$ nSamples \times nClusters\f$ matrix of results. It contains
    posterior probabilities for each sample from the input
    @param flags This parameter will be ignored
     */
    CV_WRAP virtual float predict( InputArray samples, OutputArray results=noArray(), int flags=0 ) const CV_OVERRIDE = 0;

    /** @brief Returns a likelihood logarithm value and an index of the most probable mixture component
    for the given sample.

    @param sample A sample for classification. It should be a one-channel matrix of
        \f$1 \times dims\f$ or \f$dims \times 1\f$ size.
    @param probs Optional output matrix that contains posterior probabilities of each component
        given the sample. It has \f$1 \times nclusters\f$ size and CV_64FC1 type.

    The method returns a two-element double vector. Zero element is a likelihood logarithm value for
    the sample. First element is an index of the most probable mixture component for the given
    sample.
     */
    CV_WRAP virtual Vec2d predict2(InputArray sample, OutputArray probs) const = 0;

    /** @brief Estimate the Gaussian mixture parameters from a samples set.

    This variation starts with Expectation step. Initial values of the model parameters will be
    estimated by the k-means algorithm.

    Unlike many of the ML models, %EM is an unsupervised learning algorithm and it does not take
    responses (class labels or function values) as input. Instead, it computes the *Maximum
    Likelihood Estimate* of the Gaussian mixture parameters from an input sample set, stores all the
    parameters inside the structure: \f$p_{i,k}\f$ in probs, \f$a_k\f$ in means , \f$S_k\f$ in
    covs[k], \f$\pi_k\f$ in weights , and optionally computes the output "class label" for each
    sample: \f$\texttt{labels}_i=\texttt{arg max}_k(p_{i,k}), i=1..N\f$ (indices of the most
    probable mixture component for each sample).

    The trained model can be used further for prediction, just like any other classifier. The
    trained model is similar to the NormalBayesClassifier.

    @param samples Samples from which the Gaussian mixture model will be estimated. It should be a
        one-channel matrix, each row of which is a sample. If the matrix does not have CV_64F type
        it will be converted to the inner matrix of such type for the further computing.
    @param logLikelihoods The optional output matrix that contains a likelihood logarithm value for
        each sample. It has \f$nsamples \times 1\f$ size and CV_64FC1 type.
    @param labels The optional output "class label" for each sample:
        \f$\texttt{labels}_i=\texttt{arg max}_k(p_{i,k}), i=1..N\f$ (indices of the most probable
        mixture component for each sample). It has \f$nsamples \times 1\f$ size and CV_32SC1 type.
    @param probs The optional output matrix that contains posterior probabilities of each Gaussian
        mixture component given the each sample. It has \f$nsamples \times nclusters\f$ size and
        CV_64FC1 type.
     */
    CV_WRAP virtual bool trainEM(InputArray samples,
                         OutputArray logLikelihoods=noArray(),
                         OutputArray labels=noArray(),
                         OutputArray probs=noArray()) = 0;

    /** @brief Estimate the Gaussian mixture parameters from a samples set.

    This variation starts with Expectation step. You need to provide initial means \f$a_k\f$ of
    mixture components. Optionally you can pass initial weights \f$\pi_k\f$ and covariance matrices
    \f$S_k\f$ of mixture components.

    @param samples Samples from which the Gaussian mixture model will be estimated. It should be a
        one-channel matrix, each row of which is a sample. If the matrix does not have CV_64F type
        it will be converted to the inner matrix of such type for the further computing.
    @param means0 Initial means \f$a_k\f$ of mixture components. It is a one-channel matrix of
        \f$nclusters \times dims\f$ size. If the matrix does not have CV_64F type it will be
        converted to the inner matrix of such type for the further computing.
    @param covs0 The vector of initial covariance matrices \f$S_k\f$ of mixture components. Each of
        covariance matrices is a one-channel matrix of \f$dims \times dims\f$ size. If the matrices
        do not have CV_64F type they will be converted to the inner matrices of such type for the
        further computing.
    @param weights0 Initial weights \f$\pi_k\f$ of mixture components. It should be a one-channel
        floating-point matrix with \f$1 \times nclusters\f$ or \f$nclusters \times 1\f$ size.
    @param logLikelihoods The optional output matrix that contains a likelihood logarithm value for
        each sample. It has \f$nsamples \times 1\f$ size and CV_64FC1 type.
    @param labels The optional output "class label" for each sample:
        \f$\texttt{labels}_i=\texttt{arg max}_k(p_{i,k}), i=1..N\f$ (indices of the most probable
        mixture component for each sample). It has \f$nsamples \times 1\f$ size and CV_32SC1 type.
    @param probs The optional output matrix that contains posterior probabilities of each Gaussian
        mixture component given the each sample. It has \f$nsamples \times nclusters\f$ size and
        CV_64FC1 type.
    */
    CV_WRAP virtual bool trainE(InputArray samples, InputArray means0,
                        InputArray covs0=noArray(),
                        InputArray weights0=noArray(),
                        OutputArray logLikelihoods=noArray(),
                        OutputArray labels=noArray(),
                        OutputArray probs=noArray()) = 0;

    /** @brief Estimate the Gaussian mixture parameters from a samples set.

    This variation starts with Maximization step. You need to provide initial probabilities
    \f$p_{i,k}\f$ to use this option.

    @param samples Samples from which the Gaussian mixture model will be estimated. It should be a
        one-channel matrix, each row of which is a sample. If the matrix does not have CV_64F type
        it will be converted to the inner matrix of such type for the further computing.
    @param probs0 the probabilities
    @param logLikelihoods The optional output matrix that contains a likelihood logarithm value for
        each sample. It has \f$nsamples \times 1\f$ size and CV_64FC1 type.
    @param labels The optional output "class label" for each sample:
        \f$\texttt{labels}_i=\texttt{arg max}_k(p_{i,k}), i=1..N\f$ (indices of the most probable
        mixture component for each sample). It has \f$nsamples \times 1\f$ size and CV_32SC1 type.
    @param probs The optional output matrix that contains posterior probabilities of each Gaussian
        mixture component given the each sample. It has \f$nsamples \times nclusters\f$ size and
        CV_64FC1 type.
    */
    CV_WRAP virtual bool trainM(InputArray samples, InputArray probs0,
                        OutputArray logLikelihoods=noArray(),
                        OutputArray labels=noArray(),
                        OutputArray probs=noArray()) = 0;

    /** Creates empty %EM model.
    The model should be trained then using StatModel::train(traindata, flags) method. Alternatively, you
    can use one of the EM::train\* methods or load it from file using Algorithm::load\<EM\>(filename).
     */
    CV_WRAP static Ptr<EM> create();

    /** @brief Loads and creates a serialized EM from a file
     *
     * Use EM::save to serialize and store an EM to disk.
     * Load the EM from this file again, by calling this function with the path to the file.
     * Optionally specify the node for the file containing the classifier
     *
     * @param filepath path to serialized EM
     * @param nodeName name of node containing the classifier
     */
    CV_WRAP static Ptr<EM> load(const String& filepath , const String& nodeName = String());
};

/****************************************************************************************\
*                                      Decision Tree                                     *
\****************************************************************************************/

/** @brief The class represents a single decision tree or a collection of decision trees.

The current public interface of the class allows user to train only a single decision tree, however
the class is capable of storing multiple decision trees and using them for prediction (by summing
responses or using a voting schemes), and the derived from DTrees classes (such as RTrees and Boost)
use this capability to implement decision tree ensembles.

@sa @ref ml_intro_trees
*/
class CV_EXPORTS_W DTrees : public StatModel
{
public:
    /** Predict options */
    enum Flags { PREDICT_AUTO=0, PREDICT_SUM=(1<<8), PREDICT_MAX_VOTE=(2<<8), PREDICT_MASK=(3<<8) };

    /** Cluster possible values of a categorical variable into K\<=maxCategories clusters to
    find a suboptimal split.
    If a discrete variable, on which the training procedure tries to make a split, takes more than
    maxCategories values, the precise best subset estimation may take a very long time because the
    algorithm is exponential. Instead, many decision trees engines (including our implementation)
    try to find sub-optimal split in this case by clustering all the samples into maxCategories
    clusters that is some categories are merged together. The clustering is applied only in n \>
    2-class classification problems for categorical variables with N \> max_categories possible
    values. In case of regression and 2-class classification the optimal split can be found
    efficiently without employing clustering, thus the parameter is not used in these cases.
    Default value is 10.*/
    /** @see setMaxCategories */
    CV_WRAP virtual int getMaxCategories() const = 0;
    /** @copybrief getMaxCategories @see getMaxCategories */
    CV_WRAP virtual void setMaxCategories(int val) = 0;

    /** The maximum possible depth of the tree.
    That is the training algorithms attempts to split a node while its depth is less than maxDepth.
    The root node has zero depth. The actual depth may be smaller if the other termination criteria
    are met (see the outline of the training procedure @ref ml_intro_trees "here"), and/or if the
    tree is pruned. Default value is INT_MAX.*/
    /** @see setMaxDepth */
    CV_WRAP virtual int getMaxDepth() const = 0;
    /** @copybrief getMaxDepth @see getMaxDepth */
    CV_WRAP virtual void setMaxDepth(int val) = 0;

    /** If the number of samples in a node is less than this parameter then the node will not be split.

    Default value is 10.*/
    /** @see setMinSampleCount */
    CV_WRAP virtual int getMinSampleCount() const = 0;
    /** @copybrief getMinSampleCount @see getMinSampleCount */
    CV_WRAP virtual void setMinSampleCount(int val) = 0;

    /** If CVFolds \> 1 then algorithms prunes the built decision tree using K-fold
    cross-validation procedure where K is equal to CVFolds.
    Default value is 10.*/
    /** @see setCVFolds */
    CV_WRAP virtual int getCVFolds() const = 0;
    /** @copybrief getCVFolds @see getCVFolds */
    CV_WRAP virtual void setCVFolds(int val) = 0;

    /** If true then surrogate splits will be built.
    These splits allow to work with missing data and compute variable importance correctly.
    Default value is false.
    @note currently it's not implemented.*/
    /** @see setUseSurrogates */
    CV_WRAP virtual bool getUseSurrogates() const = 0;
    /** @copybrief getUseSurrogates @see getUseSurrogates */
    CV_WRAP virtual void setUseSurrogates(bool val) = 0;

    /** If true then a pruning will be harsher.
    This will make a tree more compact and more resistant to the training data noise but a bit less
    accurate. Default value is true.*/
    /** @see setUse1SERule */
    CV_WRAP virtual bool getUse1SERule() const = 0;
    /** @copybrief getUse1SERule @see getUse1SERule */
    CV_WRAP virtual void setUse1SERule(bool val) = 0;

    /** If true then pruned branches are physically removed from the tree.
    Otherwise they are retained and it is possible to get results from the original unpruned (or
    pruned less aggressively) tree. Default value is true.*/
    /** @see setTruncatePrunedTree */
    CV_WRAP virtual bool getTruncatePrunedTree() const = 0;
    /** @copybrief getTruncatePrunedTree @see getTruncatePrunedTree */
    CV_WRAP virtual void setTruncatePrunedTree(bool val) = 0;

    /** Termination criteria for regression trees.
    If all absolute differences between an estimated value in a node and values of train samples
    in this node are less than this parameter then the node will not be split further. Default
    value is 0.01f*/
    /** @see setRegressionAccuracy */
    CV_WRAP virtual float getRegressionAccuracy() const = 0;
    /** @copybrief getRegressionAccuracy @see getRegressionAccuracy */
    CV_WRAP virtual void setRegressionAccuracy(float val) = 0;

    /** @brief The array of a priori class probabilities, sorted by the class label value.

    The parameter can be used to tune the decision tree preferences toward a certain class. For
    example, if you want to detect some rare anomaly occurrence, the training base will likely
    contain much more normal cases than anomalies, so a very good classification performance
    will be achieved just by considering every case as normal. To avoid this, the priors can be
    specified, where the anomaly probability is artificially increased (up to 0.5 or even
    greater), so the weight of the misclassified anomalies becomes much bigger, and the tree is
    adjusted properly.

    You can also think about this parameter as weights of prediction categories which determine
    relative weights that you give to misclassification. That is, if the weight of the first
    category is 1 and the weight of the second category is 10, then each mistake in predicting
    the second category is equivalent to making 10 mistakes in predicting the first category.
    Default value is empty Mat.*/
    /** @see setPriors */
    CV_WRAP virtual cv::Mat getPriors() const = 0;
    /** @copybrief getPriors @see getPriors */
    CV_WRAP virtual void setPriors(const cv::Mat &val) = 0;

    /** @brief The class represents a decision tree node.
     */
    class CV_EXPORTS Node
    {
    public:
        Node();
        double value; //!< Value at the node: a class label in case of classification or estimated
                      //!< function value in case of regression.
        int classIdx; //!< Class index normalized to 0..class_count-1 range and assigned to the
                      //!< node. It is used internally in classification trees and tree ensembles.
        int parent; //!< Index of the parent node
        int left; //!< Index of the left child node
        int right; //!< Index of right child node
        int defaultDir; //!< Default direction where to go (-1: left or +1: right). It helps in the
                        //!< case of missing values.
        int split; //!< Index of the first split
    };

    /** @brief The class represents split in a decision tree.
     */
    class CV_EXPORTS Split
    {
    public:
        Split();
        int varIdx; //!< Index of variable on which the split is created.
        bool inversed; //!< If true, then the inverse split rule is used (i.e. left and right
                       //!< branches are exchanged in the rule expressions below).
        float quality; //!< The split quality, a positive number. It is used to choose the best split.
        int next; //!< Index of the next split in the list of splits for the node
        float c; /**< The threshold value in case of split on an ordered variable.
                      The rule is:
                      @code{.none}
                      if var_value < c
                        then next_node <- left
                        else next_node <- right
                      @endcode */
        int subsetOfs; /**< Offset of the bitset used by the split on a categorical variable.
                            The rule is:
                            @code{.none}
                            if bitset[var_value] == 1
                                then next_node <- left
                                else next_node <- right
                            @endcode */
    };

    /** @brief Returns indices of root nodes
    */
    virtual const std::vector<int>& getRoots() const = 0;
    /** @brief Returns all the nodes

    all the node indices are indices in the returned vector
     */
    virtual const std::vector<Node>& getNodes() const = 0;
    /** @brief Returns all the splits

    all the split indices are indices in the returned vector
     */
    virtual const std::vector<Split>& getSplits() const = 0;
    /** @brief Returns all the bitsets for categorical splits

    Split::subsetOfs is an offset in the returned vector
     */
    virtual const std::vector<int>& getSubsets() const = 0;

    /** @brief Creates the empty model

    The static method creates empty decision tree with the specified parameters. It should be then
    trained using train method (see StatModel::train). Alternatively, you can load the model from
    file using Algorithm::load\<DTrees\>(filename).
     */
    CV_WRAP static Ptr<DTrees> create();

    /** @brief Loads and creates a serialized DTrees from a file
     *
     * Use DTree::save to serialize and store an DTree to disk.
     * Load the DTree from this file again, by calling this function with the path to the file.
     * Optionally specify the node for the file containing the classifier
     *
     * @param filepath path to serialized DTree
     * @param nodeName name of node containing the classifier
     */
    CV_WRAP static Ptr<DTrees> load(const String& filepath , const String& nodeName = String());
};

/****************************************************************************************\
*                                   Random Trees Classifier                              *
\****************************************************************************************/

/** @brief The class implements the random forest predictor.

@sa @ref ml_intro_rtrees
 */
class CV_EXPORTS_W RTrees : public DTrees
{
public:

    /** If true then variable importance will be calculated and then it can be retrieved by RTrees::getVarImportance.
    Default value is false.*/
    /** @see setCalculateVarImportance */
    CV_WRAP virtual bool getCalculateVarImportance() const = 0;
    /** @copybrief getCalculateVarImportance @see getCalculateVarImportance */
    CV_WRAP virtual void setCalculateVarImportance(bool val) = 0;

    /** The size of the randomly selected subset of features at each tree node and that are used
    to find the best split(s).
    If you set it to 0 then the size will be set to the square root of the total number of
    features. Default value is 0.*/
    /** @see setActiveVarCount */
    CV_WRAP virtual int getActiveVarCount() const = 0;
    /** @copybrief getActiveVarCount @see getActiveVarCount */
    CV_WRAP virtual void setActiveVarCount(int val) = 0;

    /** The termination criteria that specifies when the training algorithm stops.
    Either when the specified number of trees is trained and added to the ensemble or when
    sufficient accuracy (measured as OOB error) is achieved. Typically the more trees you have the
    better the accuracy. However, the improvement in accuracy generally diminishes and asymptotes
    pass a certain number of trees. Also to keep in mind, the number of tree increases the
    prediction time linearly. Default value is TermCriteria(TermCriteria::MAX_ITERS +
    TermCriteria::EPS, 50, 0.1)*/
    /** @see setTermCriteria */
    CV_WRAP virtual TermCriteria getTermCriteria() const = 0;
    /** @copybrief getTermCriteria @see getTermCriteria */
    CV_WRAP virtual void setTermCriteria(const TermCriteria &val) = 0;

    /** Returns the variable importance array.
    The method returns the variable importance vector, computed at the training stage when
    CalculateVarImportance is set to true. If this flag was set to false, the empty matrix is
    returned.
     */
    CV_WRAP virtual Mat getVarImportance() const = 0;

    /** Returns the result of each individual tree in the forest.
    In case the model is a regression problem, the method will return each of the trees'
    results for each of the sample cases. If the model is a classifier, it will return
    a Mat with samples + 1 rows, where the first row gives the class number and the
    following rows return the votes each class had for each sample.
        @param samples Array containing the samples for which votes will be calculated.
        @param results Array where the result of the calculation will be written.
        @param flags Flags for defining the type of RTrees.
    */
    CV_WRAP virtual void getVotes(InputArray samples, OutputArray results, int flags) const = 0;

    /** Returns the OOB error value, computed at the training stage when calcOOBError is set to true.
     * If this flag was set to false, 0 is returned. The OOB error is also scaled by sample weighting.
     */
#if CV_VERSION_MAJOR == 4
    CV_WRAP virtual double getOOBError() const { return 0; }
#else
    /*CV_WRAP*/ virtual double getOOBError() const = 0;
#endif

    /** Creates the empty model.
    Use StatModel::train to train the model, StatModel::train to create and train the model,
    Algorithm::load to load the pre-trained model.
     */
    CV_WRAP static Ptr<RTrees> create();

    /** @brief Loads and creates a serialized RTree from a file
     *
     * Use RTree::save to serialize and store an RTree to disk.
     * Load the RTree from this file again, by calling this function with the path to the file.
     * Optionally specify the node for the file containing the classifier
     *
     * @param filepath path to serialized RTree
     * @param nodeName name of node containing the classifier
     */
    CV_WRAP static Ptr<RTrees> load(const String& filepath , const String& nodeName = String());
};

/****************************************************************************************\
*                                   Boosted tree classifier                              *
\****************************************************************************************/

/** @brief Boosted tree classifier derived from DTrees

@sa @ref ml_intro_boost
 */
class CV_EXPORTS_W Boost : public DTrees
{
public:
    /** Type of the boosting algorithm.
    See Boost::Types. Default value is Boost::REAL. */
    /** @see setBoostType */
    CV_WRAP virtual int getBoostType() const = 0;
    /** @copybrief getBoostType @see getBoostType */
    CV_WRAP virtual void setBoostType(int val) = 0;

    /** The number of weak classifiers.
    Default value is 100. */
    /** @see setWeakCount */
    CV_WRAP virtual int getWeakCount() const = 0;
    /** @copybrief getWeakCount @see getWeakCount */
    CV_WRAP virtual void setWeakCount(int val) = 0;

    /** A threshold between 0 and 1 used to save computational time.
    Samples with summary weight \f$\leq 1 - weight_trim_rate\f$ do not participate in the *next*
    iteration of training. Set this parameter to 0 to turn off this functionality. Default value is 0.95.*/
    /** @see setWeightTrimRate */
    CV_WRAP virtual double getWeightTrimRate() const = 0;
    /** @copybrief getWeightTrimRate @see getWeightTrimRate */
    CV_WRAP virtual void setWeightTrimRate(double val) = 0;

    /** Boosting type.
    Gentle AdaBoost and Real AdaBoost are often the preferable choices. */
    enum Types {
        DISCRETE=0, //!< Discrete AdaBoost.
        REAL=1, //!< Real AdaBoost. It is a technique that utilizes confidence-rated predictions
                //!< and works well with categorical data.
        LOGIT=2, //!< LogitBoost. It can produce good regression fits.
        GENTLE=3 //!< Gentle AdaBoost. It puts less weight on outlier data points and for that
                 //!<reason is often good with regression data.
    };

    /** Creates the empty model.
    Use StatModel::train to train the model, Algorithm::load\<Boost\>(filename) to load the pre-trained model. */
    CV_WRAP static Ptr<Boost> create();

    /** @brief Loads and creates a serialized Boost from a file
     *
     * Use Boost::save to serialize and store an RTree to disk.
     * Load the Boost from this file again, by calling this function with the path to the file.
     * Optionally specify the node for the file containing the classifier
     *
     * @param filepath path to serialized Boost
     * @param nodeName name of node containing the classifier
     */
    CV_WRAP static Ptr<Boost> load(const String& filepath , const String& nodeName = String());
};

/****************************************************************************************\
*                                   Gradient Boosted Trees                               *
\****************************************************************************************/

/*class CV_EXPORTS_W GBTrees : public DTrees
{
public:
    struct CV_EXPORTS_W_MAP Params : public DTrees::Params
    {
        CV_PROP_RW int weakCount;
        CV_PROP_RW int lossFunctionType;
        CV_PROP_RW float subsamplePortion;
        CV_PROP_RW float shrinkage;

        Params();
        Params( int lossFunctionType, int weakCount, float shrinkage,
                float subsamplePortion, int maxDepth, bool useSurrogates );
    };

    enum {SQUARED_LOSS=0, ABSOLUTE_LOSS, HUBER_LOSS=3, DEVIANCE_LOSS};

    virtual void setK(int k) = 0;

    virtual float predictSerial( InputArray samples,
                                 OutputArray weakResponses, int flags) const = 0;

    static Ptr<GBTrees> create(const Params& p);
};*/

/****************************************************************************************\
*                              Artificial Neural Networks (ANN)                          *
\****************************************************************************************/

/////////////////////////////////// Multi-Layer Perceptrons //////////////////////////////

/** @brief Artificial Neural Networks - Multi-Layer Perceptrons.

Unlike many other models in ML that are constructed and trained at once, in the MLP model these
steps are separated. First, a network with the specified topology is created using the non-default
constructor or the method ANN_MLP::create. All the weights are set to zeros. Then, the network is
trained using a set of input and output vectors. The training procedure can be repeated more than
once, that is, the weights can be adjusted based on the new training data.

Additional flags for StatModel::train are available: ANN_MLP::TrainFlags.

@sa @ref ml_intro_ann
 */
class CV_EXPORTS_W ANN_MLP : public StatModel
{
public:
    /** Available training methods */
    enum TrainingMethods {
        BACKPROP=0, //!< The back-propagation algorithm.
        RPROP = 1, //!< The RPROP algorithm. See @cite RPROP93 for details.
        ANNEAL = 2 //!< The simulated annealing algorithm. See @cite Kirkpatrick83 for details.
    };

    /** Sets training method and common parameters.
    @param method Default value is ANN_MLP::RPROP. See ANN_MLP::TrainingMethods.
    @param param1 passed to setRpropDW0 for ANN_MLP::RPROP and to setBackpropWeightScale for ANN_MLP::BACKPROP and to initialT for ANN_MLP::ANNEAL.
    @param param2 passed to setRpropDWMin for ANN_MLP::RPROP and to setBackpropMomentumScale for ANN_MLP::BACKPROP and to finalT for ANN_MLP::ANNEAL.
    */
    CV_WRAP virtual void setTrainMethod(int method, double param1 = 0, double param2 = 0) = 0;

    /** Returns current training method */
    CV_WRAP virtual int getTrainMethod() const = 0;

    /** Initialize the activation function for each neuron.
    Currently the default and the only fully supported activation function is ANN_MLP::SIGMOID_SYM.
    @param type The type of activation function. See ANN_MLP::ActivationFunctions.
    @param param1 The first parameter of the activation function, \f$\alpha\f$. Default value is 0.
    @param param2 The second parameter of the activation function, \f$\beta\f$. Default value is 0.
    */
    CV_WRAP virtual void setActivationFunction(int type, double param1 = 0, double param2 = 0) = 0;

    /**  Integer vector specifying the number of neurons in each layer including the input and output layers.
    The very first element specifies the number of elements in the input layer.
    The last element - number of elements in the output layer. Default value is empty Mat.
    @sa getLayerSizes */
    CV_WRAP virtual void setLayerSizes(InputArray _layer_sizes) = 0;

    /**  Integer vector specifying the number of neurons in each layer including the input and output layers.
    The very first element specifies the number of elements in the input layer.
    The last element - number of elements in the output layer.
    @sa setLayerSizes */
    CV_WRAP virtual cv::Mat getLayerSizes() const = 0;

    /** Termination criteria of the training algorithm.
    You can specify the maximum number of iterations (maxCount) and/or how much the error could
    change between the iterations to make the algorithm continue (epsilon). Default value is
    TermCriteria(TermCriteria::MAX_ITER + TermCriteria::EPS, 1000, 0.01).*/
    /** @see setTermCriteria */
    CV_WRAP virtual TermCriteria getTermCriteria() const = 0;
    /** @copybrief getTermCriteria @see getTermCriteria */
    CV_WRAP virtual void setTermCriteria(TermCriteria val) = 0;

    /** BPROP: Strength of the weight gradient term.
    The recommended value is about 0.1. Default value is 0.1.*/
    /** @see setBackpropWeightScale */
    CV_WRAP virtual double getBackpropWeightScale() const = 0;
    /** @copybrief getBackpropWeightScale @see getBackpropWeightScale */
    CV_WRAP virtual void setBackpropWeightScale(double val) = 0;

    /** BPROP: Strength of the momentum term (the difference between weights on the 2 previous iterations).
    This parameter provides some inertia to smooth the random fluctuations of the weights. It can
    vary from 0 (the feature is disabled) to 1 and beyond. The value 0.1 or so is good enough.
    Default value is 0.1.*/
    /** @see setBackpropMomentumScale */
    CV_WRAP virtual double getBackpropMomentumScale() const = 0;
    /** @copybrief getBackpropMomentumScale @see getBackpropMomentumScale */
    CV_WRAP virtual void setBackpropMomentumScale(double val) = 0;

    /** RPROP: Initial value \f$\Delta_0\f$ of update-values \f$\Delta_{ij}\f$.
    Default value is 0.1.*/
    /** @see setRpropDW0 */
    CV_WRAP virtual double getRpropDW0() const = 0;
    /** @copybrief getRpropDW0 @see getRpropDW0 */
    CV_WRAP virtual void setRpropDW0(double val) = 0;

    /** RPROP: Increase factor \f$\eta^+\f$.
    It must be \>1. Default value is 1.2.*/
    /** @see setRpropDWPlus */
    CV_WRAP virtual double getRpropDWPlus() const = 0;
    /** @copybrief getRpropDWPlus @see getRpropDWPlus */
    CV_WRAP virtual void setRpropDWPlus(double val) = 0;

    /** RPROP: Decrease factor \f$\eta^-\f$.
    It must be \<1. Default value is 0.5.*/
    /** @see setRpropDWMinus */
    CV_WRAP virtual double getRpropDWMinus() const = 0;
    /** @copybrief getRpropDWMinus @see getRpropDWMinus */
    CV_WRAP virtual void setRpropDWMinus(double val) = 0;

    /** RPROP: Update-values lower limit \f$\Delta_{min}\f$.
    It must be positive. Default value is FLT_EPSILON.*/
    /** @see setRpropDWMin */
    CV_WRAP virtual double getRpropDWMin() const = 0;
    /** @copybrief getRpropDWMin @see getRpropDWMin */
    CV_WRAP virtual void setRpropDWMin(double val) = 0;

    /** RPROP: Update-values upper limit \f$\Delta_{max}\f$.
    It must be \>1. Default value is 50.*/
    /** @see setRpropDWMax */
    CV_WRAP virtual double getRpropDWMax() const = 0;
    /** @copybrief getRpropDWMax @see getRpropDWMax */
    CV_WRAP virtual void setRpropDWMax(double val) = 0;

    /** ANNEAL: Update initial temperature.
    It must be \>=0. Default value is 10.*/
    /** @see setAnnealInitialT */
    CV_WRAP virtual double getAnnealInitialT() const = 0;
    /** @copybrief getAnnealInitialT @see getAnnealInitialT */
    CV_WRAP virtual void setAnnealInitialT(double val) = 0;

    /** ANNEAL: Update final temperature.
    It must be \>=0 and less than initialT. Default value is 0.1.*/
    /** @see setAnnealFinalT */
    CV_WRAP virtual double getAnnealFinalT() const = 0;
    /** @copybrief getAnnealFinalT @see getAnnealFinalT */
    CV_WRAP virtual void setAnnealFinalT(double val) = 0;

    /** ANNEAL: Update cooling ratio.
    It must be \>0 and less than 1. Default value is 0.95.*/
    /** @see setAnnealCoolingRatio */
    CV_WRAP virtual double getAnnealCoolingRatio() const = 0;
    /** @copybrief getAnnealCoolingRatio @see getAnnealCoolingRatio */
    CV_WRAP virtual void setAnnealCoolingRatio(double val) = 0;

    /** ANNEAL: Update iteration per step.
    It must be \>0 . Default value is 10.*/
    /** @see setAnnealItePerStep */
    CV_WRAP virtual int getAnnealItePerStep() const = 0;
    /** @copybrief getAnnealItePerStep @see getAnnealItePerStep */
    CV_WRAP virtual void setAnnealItePerStep(int val) = 0;

    /** @brief Set/initialize anneal RNG */
    virtual void setAnnealEnergyRNG(const RNG& rng) = 0;

    /** possible activation functions */
    enum ActivationFunctions {
        /** Identity function: \f$f(x)=x\f$ */
        IDENTITY = 0,
        /** Symmetrical sigmoid: \f$f(x)=\beta*(1-e^{-\alpha x})/(1+e^{-\alpha x})\f$
        @note
        If you are using the default sigmoid activation function with the default parameter values
        fparam1=0 and fparam2=0 then the function used is y = 1.7159\*tanh(2/3 \* x), so the output
        will range from [-1.7159, 1.7159], instead of [0,1].*/
        SIGMOID_SYM = 1,
        /** Gaussian function: \f$f(x)=\beta e^{-\alpha x*x}\f$ */
        GAUSSIAN = 2,
        /** ReLU function: \f$f(x)=max(0,x)\f$ */
        RELU = 3,
        /** Leaky ReLU function: for x>0 \f$f(x)=x \f$ and x<=0 \f$f(x)=\alpha x \f$*/
        LEAKYRELU= 4
    };

    /** Train options */
    enum TrainFlags {
        /** Update the network weights, rather than compute them from scratch. In the latter case
        the weights are initialized using the Nguyen-Widrow algorithm. */
        UPDATE_WEIGHTS = 1,
        /** Do not normalize the input vectors. If this flag is not set, the training algorithm
        normalizes each input feature independently, shifting its mean value to 0 and making the
        standard deviation equal to 1. If the network is assumed to be updated frequently, the new
        training data could be much different from original one. In this case, you should take care
        of proper normalization. */
        NO_INPUT_SCALE = 2,
        /** Do not normalize the output vectors. If the flag is not set, the training algorithm
        normalizes each output feature independently, by transforming it to the certain range
        depending on the used activation function. */
        NO_OUTPUT_SCALE = 4
    };

    CV_WRAP virtual Mat getWeights(int layerIdx) const = 0;

    /** @brief Creates empty model

    Use StatModel::train to train the model, Algorithm::load\<ANN_MLP\>(filename) to load the pre-trained model.
    Note that the train method has optional flags: ANN_MLP::TrainFlags.
     */
    CV_WRAP static Ptr<ANN_MLP> create();

    /** @brief Loads and creates a serialized ANN from a file
     *
     * Use ANN::save to serialize and store an ANN to disk.
     * Load the ANN from this file again, by calling this function with the path to the file.
     *
     * @param filepath path to serialized ANN
     */
    CV_WRAP static Ptr<ANN_MLP> load(const String& filepath);

};

#ifndef DISABLE_OPENCV_3_COMPATIBILITY
typedef ANN_MLP ANN_MLP_ANNEAL;
#endif

/****************************************************************************************\
*                           Logistic Regression                                          *
\****************************************************************************************/

/** @brief Implements Logistic Regression classifier.

@sa @ref ml_intro_lr
 */
class CV_EXPORTS_W LogisticRegression : public StatModel
{
public:

    /** Learning rate. */
    /** @see setLearningRate */
    CV_WRAP virtual double getLearningRate() const = 0;
    /** @copybrief getLearningRate @see getLearningRate */
    CV_WRAP virtual void setLearningRate(double val) = 0;

    /** Number of iterations. */
    /** @see setIterations */
    CV_WRAP virtual int getIterations() const = 0;
    /** @copybrief getIterations @see getIterations */
    CV_WRAP virtual void setIterations(int val) = 0;

    /** Kind of regularization to be applied. See LogisticRegression::RegKinds. */
    /** @see setRegularization */
    CV_WRAP virtual int getRegularization() const = 0;
    /** @copybrief getRegularization @see getRegularization */
    CV_WRAP virtual void setRegularization(int val) = 0;

    /** Kind of training method used. See LogisticRegression::Methods. */
    /** @see setTrainMethod */
    CV_WRAP virtual int getTrainMethod() const = 0;
    /** @copybrief getTrainMethod @see getTrainMethod */
    CV_WRAP virtual void setTrainMethod(int val) = 0;

    /** Specifies the number of training samples taken in each step of Mini-Batch Gradient
    Descent. Will only be used if using LogisticRegression::MINI_BATCH training algorithm. It
    has to take values less than the total number of training samples. */
    /** @see setMiniBatchSize */
    CV_WRAP virtual int getMiniBatchSize() const = 0;
    /** @copybrief getMiniBatchSize @see getMiniBatchSize */
    CV_WRAP virtual void setMiniBatchSize(int val) = 0;

    /** Termination criteria of the algorithm. */
    /** @see setTermCriteria */
    CV_WRAP virtual TermCriteria getTermCriteria() const = 0;
    /** @copybrief getTermCriteria @see getTermCriteria */
    CV_WRAP virtual void setTermCriteria(TermCriteria val) = 0;

    //! Regularization kinds
    enum RegKinds {
        REG_DISABLE = -1, //!< Regularization disabled
        REG_L1 = 0, //!< %L1 norm
        REG_L2 = 1 //!< %L2 norm
    };

    //! Training methods
    enum Methods {
        BATCH = 0,
        MINI_BATCH = 1 //!< Set MiniBatchSize to a positive integer when using this method.
    };

    /** @brief Predicts responses for input samples and returns a float type.

    @param samples The input data for the prediction algorithm. Matrix [m x n], where each row
        contains variables (features) of one object being classified. Should have data type CV_32F.
    @param results Predicted labels as a column matrix of type CV_32S.
    @param flags Not used.
     */
    CV_WRAP virtual float predict( InputArray samples, OutputArray results=noArray(), int flags=0 ) const CV_OVERRIDE = 0;

    /** @brief This function returns the trained parameters arranged across rows.

    For a two class classification problem, it returns a row matrix. It returns learnt parameters of
    the Logistic Regression as a matrix of type CV_32F.
     */
    CV_WRAP virtual Mat get_learnt_thetas() const = 0;

    /** @brief Creates empty model.

    Creates Logistic Regression model with parameters given.
     */
    CV_WRAP static Ptr<LogisticRegression> create();

    /** @brief Loads and creates a serialized LogisticRegression from a file
     *
     * Use LogisticRegression::save to serialize and store an LogisticRegression to disk.
     * Load the LogisticRegression from this file again, by calling this function with the path to the file.
     * Optionally specify the node for the file containing the classifier
     *
     * @param filepath path to serialized LogisticRegression
     * @param nodeName name of node containing the classifier
     */
    CV_WRAP static Ptr<LogisticRegression> load(const String& filepath , const String& nodeName = String());
};


/****************************************************************************************\
*                        Stochastic Gradient Descent SVM Classifier                      *
\****************************************************************************************/

/*!
@brief Stochastic Gradient Descent SVM classifier

SVMSGD provides a fast and easy-to-use implementation of the SVM classifier using the Stochastic Gradient Descent approach,
as presented in @cite bottou2010large.

The classifier has following parameters:
- model type,
- margin type,
- margin regularization (\f$\lambda\f$),
- initial step size (\f$\gamma_0\f$),
- step decreasing power (\f$c\f$),
- and termination criteria.

The model type may have one of the following values: \ref SGD and \ref ASGD.

- \ref SGD is the classic version of SVMSGD classifier: every next step is calculated by the formula
  \f[w_{t+1} = w_t - \gamma(t) \frac{dQ_i}{dw} |_{w = w_t}\f]
  where
  - \f$w_t\f$ is the weights vector for decision function at step \f$t\f$,
  - \f$\gamma(t)\f$ is the step size of model parameters at the iteration \f$t\f$, it is decreased on each step by the formula
    \f$\gamma(t) = \gamma_0  (1 + \lambda  \gamma_0 t) ^ {-c}\f$
  - \f$Q_i\f$ is the target functional from SVM task for sample with number \f$i\f$, this sample is chosen stochastically on each step of the algorithm.

- \ref ASGD is Average Stochastic Gradient Descent SVM Classifier. ASGD classifier averages weights vector on each step of algorithm by the formula
\f$\widehat{w}_{t+1} = \frac{t}{1+t}\widehat{w}_{t} + \frac{1}{1+t}w_{t+1}\f$

The recommended model type is ASGD (following @cite bottou2010large).

The margin type may have one of the following values: \ref SOFT_MARGIN or \ref HARD_MARGIN.

- You should use \ref HARD_MARGIN type, if you have linearly separable sets.
- You should use \ref SOFT_MARGIN type, if you have non-linearly separable sets or sets with outliers.
- In the general case (if you know nothing about linear separability of your sets), use SOFT_MARGIN.

The other parameters may be described as follows:
- Margin regularization parameter is responsible for weights decreasing at each step and for the strength of restrictions on outliers
  (the less the parameter, the less probability that an outlier will be ignored).
  Recommended value for SGD model is 0.0001, for ASGD model is 0.00001.

- Initial step size parameter is the initial value for the step size \f$\gamma(t)\f$.
  You will have to find the best initial step for your problem.

- Step decreasing power is the power parameter for \f$\gamma(t)\f$ decreasing by the formula, mentioned above.
  Recommended value for SGD model is 1, for ASGD model is 0.75.

- Termination criteria can be TermCriteria::COUNT, TermCriteria::EPS or TermCriteria::COUNT + TermCriteria::EPS.
  You will have to find the best termination criteria for your problem.

Note that the parameters margin regularization, initial step size, and step decreasing power should be positive.

To use SVMSGD algorithm do as follows:

- first, create the SVMSGD object. The algorithm will set optimal parameters by default, but you can set your own parameters via functions setSvmsgdType(),
  setMarginType(), setMarginRegularization(), setInitialStepSize(), and setStepDecreasingPower().

- then the SVM model can be trained using the train features and the correspondent labels by the method train().

- after that, the label of a new feature vector can be predicted using the method predict().

@code
// Create empty object
cv::Ptr<SVMSGD> svmsgd = SVMSGD::create();

// Train the Stochastic Gradient Descent SVM
svmsgd->train(trainData);

// Predict labels for the new samples
svmsgd->predict(samples, responses);
@endcode

*/

class CV_EXPORTS_W SVMSGD : public cv::ml::StatModel
{
public:

    /** SVMSGD type.
    ASGD is often the preferable choice. */
    enum SvmsgdType
    {
        SGD, //!< Stochastic Gradient Descent
        ASGD //!< Average Stochastic Gradient Descent
    };

    /** Margin type.*/
    enum MarginType
    {
        SOFT_MARGIN, //!< General case, suits to the case of non-linearly separable sets, allows outliers.
        HARD_MARGIN  //!< More accurate for the case of linearly separable sets.
    };

    /**
     * @return the weights of the trained model (decision function f(x) = weights * x + shift).
    */
    CV_WRAP virtual Mat getWeights() = 0;

    /**
     * @return the shift of the trained model (decision function f(x) = weights * x + shift).
    */
    CV_WRAP virtual float getShift() = 0;

    /** @brief Creates empty model.
     * Use StatModel::train to train the model. Since %SVMSGD has several parameters, you may want to
     * find the best parameters for your problem or use setOptimalParameters() to set some default parameters.
    */
    CV_WRAP static Ptr<SVMSGD> create();

    /** @brief Loads and creates a serialized SVMSGD from a file
     *
     * Use SVMSGD::save to serialize and store an SVMSGD to disk.
     * Load the SVMSGD from this file again, by calling this function with the path to the file.
     * Optionally specify the node for the file containing the classifier
     *
     * @param filepath path to serialized SVMSGD
     * @param nodeName name of node containing the classifier
     */
    CV_WRAP static Ptr<SVMSGD> load(const String& filepath , const String& nodeName = String());

    /** @brief Function sets optimal parameters values for chosen SVM SGD model.
     * @param svmsgdType is the type of SVMSGD classifier.
     * @param marginType is the type of margin constraint.
    */
    CV_WRAP virtual void setOptimalParameters(int svmsgdType = SVMSGD::ASGD, int marginType = SVMSGD::SOFT_MARGIN) = 0;

    /** @brief %Algorithm type, one of SVMSGD::SvmsgdType. */
    /** @see setSvmsgdType */
    CV_WRAP virtual int getSvmsgdType() const = 0;
    /** @copybrief getSvmsgdType @see getSvmsgdType */
    CV_WRAP virtual void setSvmsgdType(int svmsgdType) = 0;

    /** @brief %Margin type, one of SVMSGD::MarginType. */
    /** @see setMarginType */
    CV_WRAP virtual int getMarginType() const = 0;
    /** @copybrief getMarginType @see getMarginType */
    CV_WRAP virtual void setMarginType(int marginType) = 0;

    /** @brief Parameter marginRegularization of a %SVMSGD optimization problem. */
    /** @see setMarginRegularization */
    CV_WRAP virtual float getMarginRegularization() const = 0;
    /** @copybrief getMarginRegularization @see getMarginRegularization */
    CV_WRAP virtual void setMarginRegularization(float marginRegularization) = 0;

    /** @brief Parameter initialStepSize of a %SVMSGD optimization problem. */
    /** @see setInitialStepSize */
    CV_WRAP virtual float getInitialStepSize() const = 0;
    /** @copybrief getInitialStepSize @see getInitialStepSize */
    CV_WRAP virtual void setInitialStepSize(float InitialStepSize) = 0;

    /** @brief Parameter stepDecreasingPower of a %SVMSGD optimization problem. */
    /** @see setStepDecreasingPower */
    CV_WRAP virtual float getStepDecreasingPower() const = 0;
    /** @copybrief getStepDecreasingPower @see getStepDecreasingPower */
    CV_WRAP virtual void setStepDecreasingPower(float stepDecreasingPower) = 0;

    /** @brief Termination criteria of the training algorithm.
    You can specify the maximum number of iterations (maxCount) and/or how much the error could
    change between the iterations to make the algorithm continue (epsilon).*/
    /** @see setTermCriteria */
    CV_WRAP virtual TermCriteria getTermCriteria() const = 0;
    /** @copybrief getTermCriteria @see getTermCriteria */
    CV_WRAP virtual void setTermCriteria(const cv::TermCriteria &val) = 0;
};


/****************************************************************************************\
*                           Auxiliary functions declarations                              *
\****************************************************************************************/

/** @brief Generates _sample_ from multivariate normal distribution

@param mean an average row vector
@param cov symmetric covariation matrix
@param nsamples returned samples count
@param samples returned samples array
*/
CV_EXPORTS void randMVNormal( InputArray mean, InputArray cov, int nsamples, OutputArray samples);

/** @brief Creates test set */
CV_EXPORTS void createConcentricSpheresTestSet( int nsamples, int nfeatures, int nclasses,
                                                OutputArray samples, OutputArray responses);


/****************************************************************************************\
*                                   Simulated annealing solver                             *
\****************************************************************************************/

#ifdef CV_DOXYGEN
/** @brief This class declares example interface for system state used in simulated annealing optimization algorithm.

@note This class is not defined in C++ code and can't be use directly - you need your own implementation with the same methods.
*/
struct SimulatedAnnealingSolverSystem
{
    /** Give energy value for a state of system.*/
    double energy() const;
    /** Function which change the state of system (random perturbation).*/
    void changeState();
    /** Function to reverse to the previous state. Can be called once only after changeState(). */
    void reverseState();
};
#endif // CV_DOXYGEN

/** @brief The class implements simulated annealing for optimization.

@cite Kirkpatrick83 for details

@param solverSystem optimization system (see SimulatedAnnealingSolverSystem)
@param initialTemperature initial temperature
@param finalTemperature final temperature
@param coolingRatio temperature step multiplies
@param iterationsPerStep number of iterations per temperature changing step
@param lastTemperature optional output for last used temperature
@param rngEnergy specify custom random numbers generator (cv::theRNG() by default)
*/
template<class SimulatedAnnealingSolverSystem>
int simulatedAnnealingSolver(SimulatedAnnealingSolverSystem& solverSystem,
     double initialTemperature, double finalTemperature, double coolingRatio,
     size_t iterationsPerStep,
     CV_OUT double* lastTemperature = NULL,
     cv::RNG& rngEnergy = cv::theRNG()
);

//! @} ml

}
}

#include <opencv2/ml/ml.inl.hpp>

#endif // __cplusplus
#endif // OPENCV_ML_HPP

/* End of file. */