source: trunk/yat/classifier/SVM.h @ 720

Last change on this file since 720 was 720, checked in by Jari Häkkinen, 15 years ago

Fixes #170. Almost all inlines removed, some classes have no cc file.

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