1 | #ifndef _theplu_yat_classifier_svm_ |
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2 | #define _theplu_yat_classifier_svm_ |
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3 | |
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4 | // $Id$ |
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5 | |
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6 | /* |
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7 | Copyright (C) The authors contributing to this file. |
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8 | |
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9 | This file is part of the yat library, http://lev.thep.lu.se/trac/yat |
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10 | |
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11 | The yat library is free software; you can redistribute it and/or |
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12 | modify it under the terms of the GNU General Public License as |
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13 | published by the Free Software Foundation; either version 2 of the |
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14 | License, or (at your option) any later version. |
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15 | |
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16 | The yat library is distributed in the hope that it will be useful, |
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17 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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18 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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19 | General Public License for more details. |
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20 | |
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21 | You should have received a copy of the GNU General Public License |
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22 | along with this program; if not, write to the Free Software |
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23 | Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA |
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24 | 02111-1307, USA. |
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25 | */ |
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26 | |
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27 | #include "KernelLookup.h" |
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28 | #include "SupervisedClassifier.h" |
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29 | #include "SVindex.h" |
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30 | #include "Target.h" |
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31 | #include "yat/utility/vector.h" |
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32 | |
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33 | #include <utility> |
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34 | #include <vector> |
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35 | |
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36 | namespace theplu { |
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37 | namespace yat { |
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38 | namespace classifier { |
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39 | |
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40 | class DataLookup2D; |
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41 | /// |
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42 | /// @brief Support Vector Machine |
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43 | /// |
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44 | /// |
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45 | /// |
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46 | /// Class for SVM using Keerthi's second modification of Platt's |
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47 | /// Sequential Minimal Optimization. The SVM uses all data given for |
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48 | /// training. If validation or testing is wanted this should be |
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49 | /// taken care of outside (in the kernel). |
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50 | /// |
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51 | class SVM : public SupervisedClassifier |
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52 | { |
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53 | |
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54 | public: |
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55 | /// |
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56 | /// Constructor taking the kernel and the target vector as |
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57 | /// input. |
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58 | /// |
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59 | /// @note if the @a target or @a kernel |
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60 | /// is destroyed the behaviour is undefined. |
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61 | /// |
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62 | SVM(const KernelLookup& kernel, const Target& target); |
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63 | |
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64 | /// |
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65 | /// Destructor |
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66 | /// |
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67 | virtual ~SVM(); |
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68 | |
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69 | /// |
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70 | /// If DataLookup2D is not a KernelLookup a bad_cast exception is thrown. |
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71 | /// |
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72 | SupervisedClassifier* |
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73 | make_classifier(const DataLookup2D&, const Target&) const; |
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74 | |
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75 | /// |
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76 | /// @return \f$ \alpha \f$ |
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77 | /// |
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78 | inline const utility::vector& alpha(void) const { return alpha_; } |
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79 | |
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80 | /// |
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81 | /// The C-parameter is the balance term (see train()). A very |
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82 | /// large C means the training will be focused on getting samples |
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83 | /// correctly classified, with risk for overfitting and poor |
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84 | /// generalisation. A too small C will result in a training where |
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85 | /// misclassifications are not penalized. C is weighted with |
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86 | /// respect to the size, so \f$ n_+C_+ = n_-C_- \f$, meaning a |
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87 | /// misclassificaion of the smaller group is penalized |
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88 | /// harder. This balance is equivalent to the one occuring for |
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89 | /// regression with regularisation, or ANN-training with a |
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90 | /// weight-decay term. Default is C set to infinity. |
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91 | /// |
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92 | /// @returns mean of vector \f$ C_i \f$ |
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93 | /// |
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94 | inline double C(void) const { return 1/C_inverse_; } |
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95 | |
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96 | /// |
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97 | /// Default is max_epochs set to 10,000,000. |
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98 | /// |
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99 | /// @return number of maximal epochs |
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100 | /// |
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101 | inline long int max_epochs(void) const {return max_epochs_;} |
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102 | |
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103 | /** |
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104 | The output is calculated as \f$ o_i = \sum \alpha_j t_j K_{ij} |
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105 | + bias \f$, where \f$ t \f$ is the target. |
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106 | |
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107 | @return output |
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108 | */ |
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109 | inline const theplu::yat::utility::vector& |
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110 | output(void) const { return output_; } |
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111 | |
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112 | /** |
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113 | Generate prediction @a predict from @a input. The prediction |
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114 | is calculated as the output times the margin, i.e., geometric |
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115 | distance from decision hyperplane: \f$ \frac{ \sum \alpha_j |
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116 | t_j K_{ij} + bias}{w} \f$ The output has 2 rows. The first row |
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117 | is for binary target true, and the second is for binary target |
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118 | false. The second row is superfluous as it is the first row |
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119 | negated. It exist just to be aligned with multi-class |
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120 | SupervisedClassifiers. Each column in @a input and @a output |
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121 | corresponds to a sample to predict. Each row in @a input |
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122 | corresponds to a training sample, and more exactly row i in @a |
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123 | input should correspond to row i in KernelLookup that was used |
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124 | for training. |
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125 | */ |
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126 | void predict(const DataLookup2D& input, utility::matrix& predict) const; |
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127 | |
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128 | /// |
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129 | /// @return output times margin (i.e. geometric distance from |
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130 | /// decision hyperplane) from data @a input |
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131 | /// |
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132 | double predict(const DataLookup1D& input) const; |
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133 | |
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134 | /// |
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135 | /// @return output times margin from data @a input with |
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136 | /// corresponding @a weight |
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137 | /// |
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138 | double predict(const DataLookupWeighted1D& input) const; |
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139 | |
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140 | /// |
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141 | /// Function sets \f$ \alpha=0 \f$ and makes SVM untrained. |
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142 | /// |
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143 | inline void reset(void) |
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144 | { trained_=false; alpha_=utility::vector(target_.size(),0); } |
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145 | |
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146 | /// |
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147 | /// @brief sets the C-Parameter |
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148 | /// |
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149 | void set_C(const double); |
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150 | |
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151 | /** |
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152 | Training the SVM following Platt's SMO, with Keerti's |
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153 | modifacation. Minimizing \f$ \frac{1}{2}\sum |
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154 | y_iy_j\alpha_i\alpha_j(K_{ij}+\frac{1}{C_i}\delta_{ij}) - \sum |
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155 | alpha_i\f$ , which corresponds to minimizing \f$ \sum |
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156 | w_i^2+\sum C_i\xi_i^2 \f$. |
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157 | |
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158 | @note If the training problem is not linearly separable and C |
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159 | is set to infinity, the minima will be located in the infinity, |
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160 | and thus the minumum will not be reached within the maximal |
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161 | number of epochs. More exactly, when the problem is not |
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162 | linearly separable, there exists an eigenvector to \f$ |
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163 | H_{ij}=y_iy_jK_{ij} \f$ within the space defined by the |
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164 | conditions: \f$ \alpha_i>0 \f$ and \f$ \sum \alpha_i y_i = 0 |
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165 | \f$. As the eigenvalue is zero in this direction the quadratic |
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166 | term does not contribute to the objective, but the objective |
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167 | only consists of the linear term and hence there is no |
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168 | minumum. This problem only occurs when \f$ C \f$ is set to |
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169 | infinity because for a finite \f$ C \f$ all eigenvalues are |
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170 | finite. However, for a large \f$ C \f$ (and training problem is |
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171 | non-linearly separable) there exists an eigenvector |
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172 | corresponding to a small eigenvalue, which means the minima has |
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173 | moved from infinity to "very far away". In practice this will |
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174 | also result in that the minima is not reached withing the |
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175 | maximal number of epochs and the of \f$ C \f$ should be |
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176 | decreased. |
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177 | |
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178 | @return true if succesful |
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179 | */ |
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180 | bool train(); |
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181 | |
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182 | |
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183 | |
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184 | private: |
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185 | /// |
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186 | /// Copy constructor. (not implemented) |
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187 | /// |
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188 | SVM(const SVM&); |
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189 | |
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190 | /// |
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191 | /// Calculates bounds for alpha2 |
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192 | /// |
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193 | void bounds(double&, double&) const; |
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194 | |
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195 | /// |
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196 | /// @brief calculates the bias term |
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197 | /// |
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198 | /// @return true if successful |
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199 | /// |
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200 | bool calculate_bias(void); |
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201 | |
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202 | /// |
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203 | /// Calculate margin that is inverse of w |
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204 | /// |
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205 | void calculate_margin(void); |
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206 | |
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207 | /// |
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208 | /// Private function choosing which two elements that should be |
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209 | /// updated. First checking for the biggest violation (output - target = |
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210 | /// 0) among support vectors (alpha!=0). If no violation was found check |
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211 | /// sequentially among the other samples. If no violation there as |
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212 | /// well training is completed |
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213 | /// |
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214 | /// @return true if a pair of samples that violate the conditions |
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215 | /// can be found |
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216 | /// |
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217 | bool choose(const theplu::yat::utility::vector&); |
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218 | |
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219 | /// |
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220 | /// @return kernel modified with diagonal term (soft margin) |
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221 | /// |
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222 | inline double kernel_mod(const size_t i, const size_t j) const |
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223 | { return i!=j ? (*kernel_)(i,j) : (*kernel_)(i,j) + C_inverse_; } |
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224 | |
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225 | /// @return 1 if i belong to binary target true else -1 |
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226 | inline int target(size_t i) const { return target_.binary(i) ? 1 : -1; } |
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227 | |
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228 | utility::vector alpha_; |
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229 | double bias_; |
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230 | double C_inverse_; |
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231 | const KernelLookup* kernel_; |
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232 | double margin_; |
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233 | unsigned long int max_epochs_; |
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234 | utility::vector output_; |
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235 | bool owner_; |
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236 | SVindex sample_; |
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237 | bool trained_; |
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238 | double tolerance_; |
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239 | |
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240 | }; |
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241 | |
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242 | }}} // of namespace classifier, yat, and theplu |
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243 | |
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244 | #endif |
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