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epanechnikov_kernel.hpp
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1 
12 #ifndef MLPACK_CORE_KERNELS_EPANECHNIKOV_KERNEL_HPP
13 #define MLPACK_CORE_KERNELS_EPANECHNIKOV_KERNEL_HPP
14 
15 #include <mlpack/prereqs.hpp>
17 
18 namespace mlpack {
19 namespace kernel {
20 
31 {
32  public:
38  EpanechnikovKernel(const double bandwidth = 1.0) :
39  bandwidth(bandwidth),
40  inverseBandwidthSquared(1.0 / (bandwidth * bandwidth))
41  { }
42 
51  template<typename VecTypeA, typename VecTypeB>
52  double Evaluate(const VecTypeA& a, const VecTypeB& b) const;
53 
58  double Evaluate(const double distance) const;
59 
65  double Gradient(const double distance) const;
66 
72  double GradientForSquaredDistance(const double distanceSquared) const;
82  template<typename VecTypeA, typename VecTypeB>
83  double ConvolutionIntegral(const VecTypeA& a, const VecTypeB& b);
84 
90  double Normalizer(const size_t dimension);
91 
95  template<typename Archive>
96  void Serialize(Archive& ar, const unsigned int version);
97 
98  private:
100  double bandwidth;
102  double inverseBandwidthSquared;
103 
104 };
105 
107 template<>
109 {
110  public:
112  static const bool IsNormalized = true;
114  static const bool UsesSquaredDistance = true;
115 };
116 
117 } // namespace kernel
118 } // namespace mlpack
119 
120 // Include implementation.
121 #include "epanechnikov_kernel_impl.hpp"
122 
123 #endif
This is a template class that can provide information about various kernels.
The core includes that mlpack expects; standard C++ includes and Armadillo.
double Evaluate(const VecTypeA &a, const VecTypeB &b) const
Evaluate the Epanechnikov kernel on the given two inputs.
EpanechnikovKernel(const double bandwidth=1.0)
Instantiate the Epanechnikov kernel with the given bandwidth (default 1.0).
double Normalizer(const size_t dimension)
Compute the normalizer of this Epanechnikov kernel for the given dimension.
double GradientForSquaredDistance(const double distanceSquared) const
Evaluate the Gradient of Epanechnikov kernel given that the squared distance between the two input po...
The Epanechnikov kernel, defined as.
static const bool IsNormalized
If true, then the kernel is normalized: K(x, x) = K(y, y) = 1 for all x.
double Gradient(const double distance) const
Evaluate the Gradient of Epanechnikov kernel given that the distance between the two input points is ...
void Serialize(Archive &ar, const unsigned int version)
Serialize the kernel.
static const bool UsesSquaredDistance
If true, then the kernel include a squared distance, ||x - y||^2 .
double ConvolutionIntegral(const VecTypeA &a, const VecTypeB &b)
Obtains the convolution integral [integral of K(||x-a||) K(||b-x||) dx] for the two vectors...