gaussian_kernel.hpp

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#ifndef MLPACK_CORE_KERNELS_GAUSSIAN_KERNEL_HPP
#define MLPACK_CORE_KERNELS_GAUSSIAN_KERNEL_HPP

#include <mlpack/prereqs.hpp>
#include <mlpack/core/metrics/lmetric.hpp>
#include <mlpack/core/kernels/kernel_traits.hpp>

namespace mlpack {
namespace kernel {

class GaussianKernel
{
 public:
  GaussianKernel() : bandwidth(1.0), gamma(-0.5)
  { }

  GaussianKernel(const double bandwidth) :
      bandwidth(bandwidth),
      gamma(-0.5 * pow(bandwidth, -2.0))
  { }

  template<typename VecTypeA, typename VecTypeB>
  double Evaluate(const VecTypeA& a, const VecTypeB& b) const
  {
    // The precalculation of gamma saves us a little computation time.
    return exp(gamma * metric::SquaredEuclideanDistance::Evaluate(a, b));
  }

  double Evaluate(const double t) const
  {
    // The precalculation of gamma saves us a little computation time.
    return exp(gamma * std::pow(t, 2.0));
  }

  double Gradient(const double t) const {
    return 2 * t * gamma * exp(gamma * std::pow(t, 2.0));
  }

  double GradientForSquaredDistance(const double t) const {
    return gamma * exp(gamma * t);
  }

  double Normalizer(const size_t dimension)
  {
    return pow(sqrt(2.0 * M_PI) * bandwidth, (double) dimension);
  }

  template<typename VecTypeA, typename VecTypeB>
  double ConvolutionIntegral(const VecTypeA& a, const VecTypeB& b)
  {
    return Evaluate(sqrt(metric::SquaredEuclideanDistance::Evaluate(a, b) /
        2.0)) / (Normalizer(a.n_rows) * pow(2.0, (double) a.n_rows / 2.0));
  }


  double Bandwidth() const { return bandwidth; }

  void Bandwidth(const double bandwidth)
  {
    this->bandwidth = bandwidth;
    this->gamma = -0.5 * pow(bandwidth, -2.0);
  }

  double Gamma() const { return gamma; }

  template<typename Archive>
  void serialize(Archive& ar, const uint32_t /* version */)
  {
    ar(CEREAL_NVP(bandwidth));
    ar(CEREAL_NVP(gamma));
  }

 private:
  double bandwidth;

  double gamma;
};

template<>
class KernelTraits<GaussianKernel>
{
 public:
  static const bool IsNormalized = true;
  static const bool UsesSquaredDistance = true;
};

} // namespace kernel
} // namespace mlpack

#endif