source: trunk/yat/classifier/SVM.h @ 1268

Last change on this file since 1268 was 1205, checked in by Peter, 13 years ago

fixes #75

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  • Property svn:keywords set to Author Date ID
File size: 7.2 KB
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1#ifndef _theplu_yat_classifier_svm_
2#define _theplu_yat_classifier_svm_
3
4// $Id$
5
6/*
7  Copyright (C) 2004, 2005 Jari Häkkinen, Peter Johansson
8  Copyright (C) 2006 Jari Häkkinen, Markus Ringnér, Peter Johansson
9  Copyright (C) 2007 Peter Johansson
10
11  This file is part of the yat library, http://trac.thep.lu.se/yat
12
13  The yat library is free software; you can redistribute it and/or
14  modify it under the terms of the GNU General Public License as
15  published by the Free Software Foundation; either version 2 of the
16  License, or (at your option) any later version.
17
18  The yat library is distributed in the hope that it will be useful,
19  but WITHOUT ANY WARRANTY; without even the implied warranty of
20  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
21  General Public License for more details.
22
23  You should have received a copy of the GNU General Public License
24  along with this program; if not, write to the Free Software
25  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
26  02111-1307, USA.
27*/
28
29#include "SVindex.h"
30#include "Target.h"
31#include "yat/utility/Vector.h"
32
33#include <utility>
34#include <vector>
35
36namespace theplu {
37namespace yat {
38namespace utility{
39  class Matrix;
40}
41
42namespace classifier { 
43
44  class DataLookup1D;
45  class DataLookupWeighted1D;
46  class KernelLookup;
47
48  /**
49     \brief Support Vector Machine
50  */
51  class SVM
52  {
53 
54  public:
55    ///
56    /// \brief Constructor
57    ///
58    SVM(void);
59
60    /**
61       \brief Copy constructor.
62    */ 
63    SVM(const SVM&);
64         
65    ///
66    /// \brief Destructor
67    ///
68    virtual ~SVM();
69
70    /**
71       \brief Create an untrained copy of SVM.
72
73       \returns A dynamically allocated SVM, which has to be deleted
74       by the caller to avoid memory leaks.
75    */
76    SVM* make_classifier(void) const;
77
78    ///
79    /// @return alpha parameters
80    ///
81    const utility::Vector& alpha(void) const;
82
83    ///
84    /// The C-parameter is the balance term (see train()). A very
85    /// large C means the training will be focused on getting samples
86    /// correctly classified, with risk for overfitting and poor
87    /// generalisation. A too small C will result in a training, in
88    /// which misclassifications are not penalized. C is weighted with
89    /// respect to the size such that \f$ n_+C_+ = n_-C_- \f$, meaning
90    /// a misclassificaion of the smaller group is penalized
91    /// harder. This balance is equivalent to the one occuring for
92    /// %regression with regularisation, or ANN-training with a
93    /// weight-decay term. Default is C set to infinity.
94    ///
95    /// @returns mean of vector \f$ C_i \f$
96    ///
97    double C(void) const;
98
99    ///
100    /// Default is max_epochs set to 100,000.
101    ///
102    /// @return number of maximal epochs
103    ///
104    long int max_epochs(void) const;
105   
106    /**
107      \brief set maximal number of epochs in training
108    */
109    void max_epochs(long int);
110   
111    /**
112        The output is calculated as \f$ o_i = \sum \alpha_j t_j K_{ij}
113        + bias \f$, where \f$ t \f$ is the target.
114   
115        @return output of training samples
116    */ 
117    const theplu::yat::utility::Vector& output(void) const;
118
119    /**
120       Generate prediction @a predict from @a input. The prediction
121       is calculated as the output times the margin, i.e., geometric
122       distance from decision hyperplane: \f$ \frac{ \sum \alpha_j
123       t_j K_{ij} + bias}{|w|} \f$ The output has 2 rows. The first row
124       is for binary target true, and the second is for binary target
125       false. The second row is superfluous as it is the first row
126       negated. It exist just to be aligned with multi-class
127       SupervisedClassifiers. Each column in @a input and @a output
128       corresponds to a sample to predict. Each row in @a input
129       corresponds to a training sample, and more exactly row i in @a
130       input should correspond to row i in KernelLookup that was used
131       for training.
132    */
133    void predict(const KernelLookup& input, utility::Matrix& predict) const;
134
135    /*
136    ///
137    /// @return output times margin (i.e. geometric distance from
138    /// decision hyperplane) from data @a input
139    ///
140    double predict(const DataLookup1D& input) const;
141
142    ///
143    /// @return output times margin from data @a input with
144    /// corresponding @a weight
145    ///
146    double predict(const DataLookupWeighted1D& input) const;
147    */
148
149    ///
150    /// @brief sets the C-Parameter
151    ///
152    void set_C(const double);
153
154    /**
155       Training the SVM following Platt's SMO, with Keerti's
156       modifacation. Minimizing \f$ \frac{1}{2}\sum
157       y_iy_j\alpha_i\alpha_j(K_{ij}+\frac{1}{C_i}\delta_{ij}) - \sum
158       \alpha_i\f$, which corresponds to minimizing \f$ \sum
159       w_i^2+\sum C_i\xi_i^2 \f$.
160
161       @note If the training problem is not linearly separable and C
162       is set to infinity, the minima will be located in the infinity,
163       and thus the minimum will not be reached within the maximal
164       number of epochs. More exactly, when the problem is not
165       linearly separable, there exists an eigenvector to \f$
166       H_{ij}=y_iy_jK_{ij} \f$ within the space defined by the
167       conditions: \f$ \alpha_i>0 \f$ and \f$ \sum \alpha_i y_i = 0
168       \f$. As the eigenvalue is zero in this direction the quadratic
169       term does not contribute to the objective, but the objective
170       only consists of the linear term and hence there is no
171       minumum. This problem only occurs when \f$ C \f$ is set to
172       infinity because for a finite \f$ C \f$ all eigenvalues are
173       finite. However, for a large \f$ C \f$ (and training problem is
174       non-linearly separable) there exists an eigenvector
175       corresponding to a small eigenvalue, which means the minima has
176       moved from infinity to "very far away". In practice this will
177       also result in that the minima is not reached withing the
178       maximal number of epochs and the of \f$ C \f$ should be
179       decreased.
180
181       Class for SVM using Keerthi's second modification of Platt's
182       Sequential Minimal Optimization. The SVM uses all data given for
183       training.
184       
185       \throw std::runtime_error if maximal number of epoch is reach.
186    */
187    void train(const KernelLookup& kernel, const Target& target);
188
189       
190     
191  private:
192    ///
193    /// Calculates bounds for alpha2
194    ///
195    void bounds(double&, double&) const;
196
197    ///
198    /// @brief calculates the bias term
199    ///
200    /// @return true if successful
201    ///
202    void calculate_bias(void);
203
204    ///
205    /// Calculate margin that is inverse of w
206    ///
207    void calculate_margin(void);
208
209    ///
210    ///   Private function choosing which two elements that should be
211    ///   updated. First checking for the biggest violation (output - target =
212    ///   0) among support vectors (alpha!=0). If no violation was found check
213    ///   sequentially among the other samples. If no violation there as
214    ///   well training is completed
215    ///
216    ///  @return true if a pair of samples that violate the conditions
217    ///  can be found
218    ///
219    bool choose(const theplu::yat::utility::Vector&);
220
221    ///
222    /// @return kernel modified with diagonal term (soft margin)
223    ///
224    double kernel_mod(const size_t i, const size_t j) const;
225
226    ///
227    /// @return 1 if i belong to binary target true else -1
228    ///
229    int target(size_t i) const;
230
231    utility::Vector alpha_;
232    double bias_;
233    double C_inverse_;
234    // not owned by SVM
235    const KernelLookup* kernel_; 
236    double margin_;
237    unsigned long int max_epochs_;
238    utility::Vector output_;
239    SVindex sample_;
240    Target target_;
241    double tolerance_;
242    bool trained_;
243
244  };
245
246}}} // of namespace classifier, yat, and theplu
247
248#endif
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