FisherLDA.h

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//===========================================================================
/*!
 * 
 *
 * \brief       FisherLDA
 * 
 * 
 *
 * \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_FISHERLDA_H
#define SHARK_ALGORITHMS_TRAINERS_FISHERLDA_H
 
#include <shark/Core/DLLSupport.h>
#include <shark/Models/LinearModel.h>
#include <shark/Algorithms/Trainers/AbstractTrainer.h>
 
namespace shark {
 
 
/// \brief Fisher's Linear Discriminant Analysis for data compression
///
/// Similar to PCA, \em Fisher's \em Linear \em Discriminant \em Analysis is a
/// method for reducing the datas dimensionality. In contrast to PCA it also uses
/// class information.
///
/// Consider the data's covariance matrix \f$ S \f$ and a unit vector \f$ u \f$
/// which defines a one-dimensional subspace of the data. Then, PCA would
/// maximmize the objective \f$ J(u) = u^T S u \f$, namely the datas variance in
/// the subspace. Fisher-LDA, however, maximizes
/// \f[
///   J(u) = ( u^T S_W u )^{-1} ( u^T S_B u ),
/// \f]
/// where \f$ S_B \f$ is the covariance matrix of the class-means and \f$ S_W \f$
/// is the average covariance matrix of all classes (in both cases, each class'
/// influence is weighted by it's size). As a result, Fisher-LDA finds a subspace
/// in which the class means are wide-spread while (in average) the variance of
/// each class becomes small. This leads to good lower-dimensional
/// representations of the data in cases where the classes are linearly
/// separable.
///
/// If a subspace with more than one dimension is requested, the above step is
/// executed consecutively to find the next optimal subspace-dimension
/// orthogonally to the others.
///
///
/// \b Note: the max. dimensionality for the subspace is \#NumOfClasses-1.
///
/// It is possible to choose how many dimnsions are used by setting the appropriate value
/// by calling setSubspaceDImension or in the constructor.
/// Also optionally whitening can be applied.
/// For more detailed information about Fisher-LDA, see \e Bishop, \e Pattern
/// \e Recognition \e and \e Machine \e Learning.
/// \ingroup supervised_trainer
class FisherLDA : public AbstractTrainer<LinearModel<>, unsigned int>
{
public:
    /// Constructor
    SHARK_EXPORT_SYMBOL FisherLDA(bool whitening = false, std::size_t subspaceDimension = 0);
 
    /// \brief From INameable: return the class name.
    std::string name() const
    { return "Fisher-LDA"; }
 
    void setSubspaceDimensions(std::size_t dimensions){
        m_subspaceDimensions = dimensions;
    }
    
    std::size_t subspaceDimensions()const{
        return m_subspaceDimensions;
    }
 
    /// check whether whitening mode is on
    bool whitening() const{ 
        return m_whitening; 
    }
 
    /// if active, the model whitenes the inputs
    void setWhitening(bool newWhitening){ 
        m_whitening = newWhitening; 
    }
 
    /// Compute the FisherLDA solution for a multi-class problem.
    SHARK_EXPORT_SYMBOL void train(LinearModel<>& model, LabeledData<RealVector, unsigned int> const& dataset);
 
protected:
    SHARK_EXPORT_SYMBOL void meanAndScatter(LabeledData<RealVector, unsigned int> const& dataset, RealVector& mean, RealMatrix& scatter);
    bool m_whitening;
    std::size_t m_subspaceDimensions;
};
 
 
}
#endif