gaussian_kernel.hpp
Go to the documentation of this file.
1 
14 #ifndef MLPACK_CORE_KERNELS_GAUSSIAN_KERNEL_HPP
15 #define MLPACK_CORE_KERNELS_GAUSSIAN_KERNEL_HPP
16 
17 #include <mlpack/prereqs.hpp>
20 
21 namespace mlpack {
22 namespace kernel {
23 
35 {
36  public:
40  GaussianKernel() : bandwidth(1.0), gamma(-0.5)
41  { }
42 
48  GaussianKernel(const double bandwidth) :
49  bandwidth(bandwidth),
50  gamma(-0.5 * pow(bandwidth, -2.0))
51  { }
52 
64  template<typename VecTypeA, typename VecTypeB>
65  double Evaluate(const VecTypeA& a, const VecTypeB& b) const
66  {
67  // The precalculation of gamma saves us a little computation time.
68  return exp(gamma * metric::SquaredEuclideanDistance::Evaluate(a, b));
69  }
70 
78  double Evaluate(const double t) const
79  {
80  // The precalculation of gamma saves us a little computation time.
81  return exp(gamma * std::pow(t, 2.0));
82  }
83 
92  double Gradient(const double t) const {
93  return 2 * t * gamma * exp(gamma * std::pow(t, 2.0));
94  }
95 
104  double GradientForSquaredDistance(const double t) const {
105  return gamma * exp(gamma * t);
106  }
107 
114  double Normalizer(const size_t dimension)
115  {
116  return pow(sqrt(2.0 * M_PI) * bandwidth, (double) dimension);
117  }
118 
126  template<typename VecTypeA, typename VecTypeB>
127  double ConvolutionIntegral(const VecTypeA& a, const VecTypeB& b)
128  {
130  2.0)) / (Normalizer(a.n_rows) * pow(2.0, (double) a.n_rows / 2.0));
131  }
132 
133 
135  double Bandwidth() const { return bandwidth; }
136 
139  void Bandwidth(const double bandwidth)
140  {
141  this->bandwidth = bandwidth;
142  this->gamma = -0.5 * pow(bandwidth, -2.0);
143  }
144 
146  double Gamma() const { return gamma; }
147 
149  template<typename Archive>
150  void serialize(Archive& ar, const unsigned int /* version */)
151  {
152  ar & BOOST_SERIALIZATION_NVP(bandwidth);
153  ar & BOOST_SERIALIZATION_NVP(gamma);
154  }
155 
156  private:
158  double bandwidth;
159 
162  double gamma;
163 };
164 
166 template<>
168 {
169  public:
171  static const bool IsNormalized = true;
173  static const bool UsesSquaredDistance = true;
174 };
175 
176 } // namespace kernel
177 } // namespace mlpack
178 
179 #endif
double Bandwidth() const
Get the bandwidth.
void serialize(Archive &ar, const unsigned int)
Serialize the kernel.
This is a template class that can provide information about various kernels.
double GradientForSquaredDistance(const double t) const
Evaluation of the gradient of Gaussian kernel given the squared distance between two points...
Linear algebra utility functions, generally performed on matrices or vectors.
Definition: add_to_po.hpp:21
The core includes that mlpack expects; standard C++ includes and Armadillo.
#define M_PI
Definition: prereqs.hpp:39
double Gradient(const double t) const
Evaluation of the gradient of Gaussian kernel given the distance between two points.
static VecTypeA::elem_type Evaluate(const VecTypeA &a, const VecTypeB &b)
Computes the distance between two points.
double Evaluate(const double t) const
Evaluation of the Gaussian kernel given the distance between two points.
GaussianKernel(const double bandwidth)
Construct the Gaussian kernel with a custom bandwidth.
GaussianKernel()
Default constructor; sets bandwidth to 1.0.
double Gamma() const
Get the precalculated constant.
double ConvolutionIntegral(const VecTypeA &a, const VecTypeB &b)
Obtain a convolution integral of the Gaussian kernel.
double Evaluate(const VecTypeA &a, const VecTypeB &b) const
Evaluation of the Gaussian kernel.
The standard Gaussian kernel.
void Bandwidth(const double bandwidth)
Modify the bandwidth.
double Normalizer(const size_t dimension)
Obtain the normalization constant of the Gaussian kernel.