DifferenceKernelMatrix.h
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1 //===========================================================================
2 /*!
3  *
4  *
5  * \brief Kernel matrix for SVM ranking.
6  *
7  *
8  * \par
9  *
10  *
11  *
12  * \author T. Glasmachers
13  * \date 2016
14  *
15  *
16  * \par Copyright 1995-2017 Shark Development Team
17  *
18  * <BR><HR>
19  * This file is part of Shark.
20  * <http://shark-ml.org/>
21  *
22  * Shark is free software: you can redistribute it and/or modify
23  * it under the terms of the GNU Lesser General Public License as published
24  * by the Free Software Foundation, either version 3 of the License, or
25  * (at your option) any later version.
26  *
27  * Shark is distributed in the hope that it will be useful,
28  * but WITHOUT ANY WARRANTY; without even the implied warranty of
29  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
30  * GNU Lesser General Public License for more details.
31  *
32  * You should have received a copy of the GNU Lesser General Public License
33  * along with Shark. If not, see <http://www.gnu.org/licenses/>.
34  *
35  */
36 //===========================================================================
37 
38 
39 #ifndef SHARK_LINALG_DIFFERENCEKERNELMATRIX_H
40 #define SHARK_LINALG_DIFFERENCEKERNELMATRIX_H
41 
42 #include <shark/Data/Dataset.h>
43 #include <shark/Data/DataView.h>
44 #include <shark/LinAlg/Base.h>
45 
46 #include <vector>
47 #include <utility>
48 #include <cmath>
49 
50 
51 namespace shark {
52 
53 
54 ///
55 /// \brief SVM ranking matrix
56 ///
57 /// \par
58 /// The DifferenceKernelMatrix class is kernel matrix with entries of
59 /// the form \f$ K_{i,j} = k(g_i, g_j) - k(g_i, s_j) - k(s_i, g_j) + k(s_i, s_j) \f$
60 /// where for data consisting of pairs of point \f$ (g_i, s_i) \f$.
61 /// This matrix form is needed in SVM ranking problems.
62 ///
63 template <class InputType, class CacheType>
64 class DifferenceKernelMatrix
65 {
66 public:
67  typedef CacheType QpFloatType;
68 
69  /// Constructor.
70  DifferenceKernelMatrix(
71  AbstractKernelFunction<InputType> const& kernel,
72  Data<InputType> const& dataset,
73  std::vector<std::pair<std::size_t, std::size_t>> const& pairs)
74  : m_kernel(kernel)
75  , m_dataset(dataset)
76  , m_indices(pairs.size())
77  {
78  DataView< Data<InputType> const > view(dataset);
79  for (std::size_t i=0; i<pairs.size(); i++)
80  {
81  std::pair<std::size_t, std::size_t> const& p = pairs[i];
82  m_indices[i] = std::make_tuple(
83  view.batch(p.first), view.positionInBatch(p.first),
84  view.batch(p.second), view.positionInBatch(p.second));
85  }
86  }
87 
88 
89  /// return a single matrix entry
90  QpFloatType operator () (std::size_t i, std::size_t j) const
91  { return entry(i, j); }
92 
93  /// return a single matrix entry
94  QpFloatType entry(std::size_t i, std::size_t j) const
95  {
96  std::tuple<std::size_t, std::size_t, std::size_t, std::size_t> const& pi = m_indices[i];
97  std::tuple<std::size_t, std::size_t, std::size_t, std::size_t> const& pj = m_indices[j];
98  std::size_t batch_si = std::get<0>(pi);
99  std::size_t index_si = std::get<1>(pi);
100  std::size_t batch_gi = std::get<2>(pi);
101  std::size_t index_gi = std::get<3>(pi);
102  std::size_t batch_sj = std::get<0>(pj);
103  std::size_t index_sj = std::get<1>(pj);
104  std::size_t batch_gj = std::get<2>(pj);
105  std::size_t index_gj = std::get<3>(pj);
106  typedef typename Data<InputType>::const_element_reference reference;
107  reference si = getBatchElement(m_dataset.batch(batch_si), index_si);
108  reference gi = getBatchElement(m_dataset.batch(batch_gi), index_gi);
109  reference sj = getBatchElement(m_dataset.batch(batch_sj), index_sj);
110  reference gj = getBatchElement(m_dataset.batch(batch_gj), index_gj);
111  double k_gi_gj = m_kernel(gi, gj);
112  double k_gi_sj = m_kernel(gi, sj);
113  double k_si_gj = m_kernel(si, gj);
114  double k_si_sj = m_kernel(si, sj);
115  return (k_gi_gj - k_gi_sj - k_si_gj + k_si_sj);
116  }
117 
118  /// \brief Computes the i-th row of the kernel matrix.
119  ///
120  /// The entries start,...,end of the i-th row are computed and stored in storage.
121  /// There must be enough room for this operation preallocated.
122  void row(std::size_t i, std::size_t start, std::size_t end, QpFloatType* storage) const {
123  for (std::size_t j = start; j < end; j++) storage[j-start] = entry(i, j);
124  }
125 
126  /// \brief Computes the kernel-matrix
127  template<class M>
128  void matrix(blas::matrix_expression<M, blas::cpu_tag>& storage) const {
129  for (std::size_t i = 0; i != size(); ++i) {
130  for (std::size_t j = 0; j != size(); ++j) {
131  storage()(i, j) = entry(i, j);
132  }
133  }
134  }
135 
136  /// swap two variables
137  void flipColumnsAndRows(std::size_t i, std::size_t j)
138  {
139  using namespace std;
140  swap(m_indices[i], m_indices[j]);
141  }
142 
143  /// return the size of the quadratic matrix
144  std::size_t size() const
145  { return m_indices.size(); }
146 
147 protected:
148  /// underlying kernel function
149  AbstractKernelFunction<InputType> const& m_kernel;
150 
151  /// underlying set of points
152  Data<InputType> const& m_dataset;
153 
154  /// pairs of points defining the matrix components
155  std::vector<std::tuple<std::size_t, std::size_t, std::size_t, std::size_t>> m_indices;
156 };
157 
158 }
159 #endif