spherical_kernel.hpp

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#ifndef MLPACK_CORE_KERNELS_SPHERICAL_KERNEL_HPP
#define MLPACK_CORE_KERNELS_SPHERICAL_KERNEL_HPP

#include <boost/math/special_functions/gamma.hpp>
#include <mlpack/prereqs.hpp>

namespace mlpack {
namespace kernel {

class SphericalKernel
{
 public:
  SphericalKernel(const double bandwidth = 1.0) :
    bandwidth(bandwidth),
    bandwidthSquared(std::pow(bandwidth, 2.0))
  { /* Nothing to do. */ }

  template<typename VecTypeA, typename VecTypeB>
  double Evaluate(const VecTypeA& a, const VecTypeB& b) const
  {
    return
        (metric::SquaredEuclideanDistance::Evaluate(a, b) <= bandwidthSquared) ?
        1.0 : 0.0;
  }
  template<typename VecTypeA, typename VecTypeB>
  double ConvolutionIntegral(const VecTypeA& a, const VecTypeB& b) const
  {
    double distance = sqrt(metric::SquaredEuclideanDistance::Evaluate(a, b));
    if (distance >= 2.0 * bandwidth)
    {
      return 0.0;
    }
    double volumeSquared = pow(Normalizer(a.n_rows), 2.0);

    switch (a.n_rows)
    {
      case 1:
        return 1.0 / volumeSquared * (2.0 * bandwidth - distance);
        break;
      case 2:
        return 1.0 / volumeSquared *
          (2.0 * bandwidth * bandwidth * acos(distance/(2.0 * bandwidth)) -
          distance / 4.0 * sqrt(4.0*bandwidth*bandwidth-distance*distance));
        break;
      default:
        Log::Fatal << "The spherical kernel does not support convolution\
          integrals above dimension two, yet..." << std::endl;
        return -1.0;
        break;
    }
  }
  double Normalizer(size_t dimension) const
  {
    return pow(bandwidth, (double) dimension) * pow(M_PI, dimension / 2.0) /
        std::tgamma(dimension / 2.0 + 1.0);
  }

  double Evaluate(const double t) const
  {
    return (t <= bandwidth) ? 1.0 : 0.0;
  }
  double Gradient(double t)
  {
    return t == bandwidth ? arma::datum::nan : 0.0;
  }

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

 private:
  double bandwidth;
  double bandwidthSquared;
};

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

} // namespace kernel
} // namespace mlpack

#endif