LDA.h

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//===========================================================================
/*!
 * 
 *
 * \brief       LDA
 * 
 * 
 *
 * \author      O. Krause
 * \date        2010
 *
 *
 * \par Copyright 1995-2017 Shark Development Team
 * 
 * <BR><HR>
 * This file is part of Shark.
 * <https://shark-ml.github.io/Shark/>
 * 
 * Shark is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published 
 * by the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 * 
 * Shark is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public License
 * along with Shark.  If not, see <http://www.gnu.org/licenses/>.
 *
 */
//===========================================================================
#ifndef SHARK_ALGORITHMS_TRAINERS_LDA_H
#define SHARK_ALGORITHMS_TRAINERS_LDA_H
 
#include <shark/Core/DLLSupport.h>
#include <shark/Core/IParameterizable.h>
#include <shark/Models/LinearModel.h>
#include <shark/Algorithms/Trainers/AbstractWeightedTrainer.h>
 
namespace shark {
 
 
///
/// \brief Linear Discriminant Analysis (LDA)
///
/// This classes implements the well known linear discriminant analysis. LDA assumes that
/// every point is drawn from a multivariate normal distributions. Every class has its own mean
/// but all classes have the same covariance.
///
/// An arbitrary number of classes is supported. The resulting model is of the form
/// \f[ \arg \max_c \log(p(x|c)*P(c)) \f]
/// where \f$ p(x|c) = \exp(-(x-m_c)^T(C+\alpha I)(x-m_c)) \f$.
/// \f$ m_c\f$ are the means of class c, \f$ C \f$ is the covariance matrix formed by all data points.
/// The regularization paramter \f$ \alpha \f$ is by default 0. The trainer is implemented such, that
/// it still works when C is singular, in this case the singular directions are ignored. 
/// \ingroup supervised_trainer
class LDA : public AbstractWeightedTrainer<LinearClassifier<>, unsigned int>, public IParameterizable<>
{
public:
    /// constructor
    LDA(double regularization = 0.0){
        setRegularization(regularization);
    }
 
    /// \brief From INameable: return the class name.
    std::string name() const
    { return "Linear Discriminant Analysis (LDA)"; }
 
    /// return the regularization constant
    double regularization()const{
        return m_regularization;
    }
 
    /// set the regularization constant. 0 means no regularization.
    void setRegularization(double regularization) {
        RANGE_CHECK(regularization >= 0.0);
        m_regularization = regularization;
    }
 
    /// inherited from IParameterizable; read the regularization parameter
    RealVector parameterVector() const {
        RealVector param(1);
        param(0) = m_regularization;
        return param;
    }
    /// inherited from IParameterizable; set the regularization parameter
    void setParameterVector(RealVector const& param) {
        SIZE_CHECK(param.size() == 1);
        m_regularization = param(0);
    }
    /// inherited from IParameterizable
    size_t numberOfParameters() const {
        return 1;
    }
 
    /// Compute the LDA solution for a multi-class problem.
    SHARK_EXPORT_SYMBOL void train(LinearClassifier<>& model, LabeledData<RealVector, unsigned int> const& dataset);
    /// Compute the LDA solution for a weighted multi-class problem.
    SHARK_EXPORT_SYMBOL void train(LinearClassifier<>& model, WeightedLabeledData<RealVector, unsigned int> const& dataset);
 
protected:
    ///The regularization parameter \f$ \lambda \f$ adds
    /// \f$ - \lambda I \f$ to the second moment matrix, where
    /// \f$ I \f$ is the identity matrix
    double m_regularization;
};
 
}
#endif