FisherLDA.h
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1 //===========================================================================
2 /*!
3  *
4  *
5  * \brief FisherLDA
6  *
7  *
8  *
9  * \author O. Krause
10  * \date 2010
11  *
12  *
13  * \par Copyright 1995-2017 Shark Development Team
14  *
15  * <BR><HR>
16  * This file is part of Shark.
17  * <http://shark-ml.org/>
18  *
19  * Shark is free software: you can redistribute it and/or modify
20  * it under the terms of the GNU Lesser General Public License as published
21  * by the Free Software Foundation, either version 3 of the License, or
22  * (at your option) any later version.
23  *
24  * Shark is distributed in the hope that it will be useful,
25  * but WITHOUT ANY WARRANTY; without even the implied warranty of
26  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
27  * GNU Lesser General Public License for more details.
28  *
29  * You should have received a copy of the GNU Lesser General Public License
30  * along with Shark. If not, see <http://www.gnu.org/licenses/>.
31  *
32  */
33 //===========================================================================
34 #ifndef SHARK_ALGORITHMS_TRAINERS_FISHERLDA_H
35 #define SHARK_ALGORITHMS_TRAINERS_FISHERLDA_H
36 
37 #include <shark/Core/DLLSupport.h>
38 #include <shark/Models/LinearModel.h>
39 #include <shark/Algorithms/Trainers/AbstractTrainer.h>
40 
41 namespace shark {
42 
43 
44 /*!
45  * \brief Fisher's Linear Discriminant Analysis for data compression
46  *
47  * Similar to PCA, \em Fisher's \em Linear \em Discriminant \em Analysis is a
48  * method for reducing the datas dimensionality. In contrast to PCA it also uses
49  * class information.
50  *
51  * Consider the data's covariance matrix \f$ S \f$ and a unit vector \f$ u \f$
52  * which defines a one-dimensional subspace of the data. Then, PCA would
53  * maximmize the objective \f$ J(u) = u^T S u \f$, namely the datas variance in
54  * the subspace. Fisher-LDA, however, maximizes
55  * \f[
56  * J(u) = ( u^T S_W u )^{-1} ( u^T S_B u ),
57  * \f]
58  * where \f$ S_B \f$ is the covariance matrix of the class-means and \f$ S_W \f$
59  * is the average covariance matrix of all classes (in both cases, each class'
60  * influence is weighted by it's size). As a result, Fisher-LDA finds a subspace
61  * in which the class means are wide-spread while (in average) the variance of
62  * each class becomes small. This leads to good lower-dimensional
63  * representations of the data in cases where the classes are linearly
64  * separable.
65  *
66  * If a subspace with more than one dimension is requested, the above step is
67  * executed consecutively to find the next optimal subspace-dimension
68  * orthogonally to the others.
69  *
70  *
71  * \b Note: the max. dimensionality for the subspace is \#NumOfClasses-1.
72  *
73  * It is possible to choose how many dimnsions are used by setting the appropriate value
74  * by calling setSubspaceDImension or in the constructor.
75  * Also optionally whitening can be applied.
76  * For more detailed information about Fisher-LDA, see \e Bishop, \e Pattern
77  * \e Recognition \e and \e Machine \e Learning.
78  */
79 class FisherLDA : public AbstractTrainer<LinearModel<>, unsigned int>
80 {
81 public:
82  /// Constructor
83  SHARK_EXPORT_SYMBOL FisherLDA(bool whitening = false, std::size_t subspaceDimension = 0);
84 
85  /// \brief From INameable: return the class name.
86  std::string name() const
87  { return "Fisher-LDA"; }
88 
89  void setSubspaceDimensions(std::size_t dimensions){
90  m_subspaceDimensions = dimensions;
91  }
92 
93  std::size_t subspaceDimensions()const{
94  return m_subspaceDimensions;
95  }
96 
97  /// check whether whitening mode is on
98  bool whitening() const{
99  return m_whitening;
100  }
101 
102  /// if active, the model whitenes the inputs
103  void setWhitening(bool newWhitening){
104  m_whitening = newWhitening;
105  }
106 
107  /// Compute the FisherLDA solution for a multi-class problem.
108  SHARK_EXPORT_SYMBOL void train(LinearModel<>& model, LabeledData<RealVector, unsigned int> const& dataset);
109 
110 protected:
111  SHARK_EXPORT_SYMBOL void meanAndScatter(LabeledData<RealVector, unsigned int> const& dataset, RealVector& mean, RealMatrix& scatter);
112  bool m_whitening;
113  std::size_t m_subspaceDimensions;
114 };
115 
116 
117 }
118 #endif