14#ifndef MLPACK_CORE_KERNELS_GAUSSIAN_KERNEL_HPP
15#define MLPACK_CORE_KERNELS_GAUSSIAN_KERNEL_HPP
50 gamma(-0.5 * pow(bandwidth, -2.0))
64 template<
typename VecTypeA,
typename VecTypeB>
65 double Evaluate(
const VecTypeA& a,
const VecTypeB& b)
const
81 return exp(gamma * std::pow(t, 2.0));
93 return 2 * t * gamma * exp(gamma * std::pow(t, 2.0));
105 return gamma * exp(gamma * t);
116 return pow(sqrt(2.0 *
M_PI) * bandwidth, (
double) dimension);
126 template<
typename VecTypeA,
typename VecTypeB>
130 2.0)) / (
Normalizer(a.n_rows) * pow(2.0, (
double) a.n_rows / 2.0));
141 this->bandwidth = bandwidth;
142 this->gamma = -0.5 * pow(bandwidth, -2.0);
146 double Gamma()
const {
return gamma; }
149 template<
typename Archive>
152 ar & BOOST_SERIALIZATION_NVP(bandwidth);
153 ar & BOOST_SERIALIZATION_NVP(gamma);
The standard Gaussian kernel.
double Evaluate(const double t) const
Evaluation of the Gaussian kernel given the distance between two points.
GaussianKernel()
Default constructor; sets bandwidth to 1.0.
double Gradient(const double t) const
Evaluation of the gradient of Gaussian kernel given the distance between two points.
void Bandwidth(const double bandwidth)
Modify the bandwidth.
double GradientForSquaredDistance(const double t) const
Evaluation of the gradient of Gaussian kernel given the squared distance between two points.
double Evaluate(const VecTypeA &a, const VecTypeB &b) const
Evaluation of the Gaussian kernel.
GaussianKernel(const double bandwidth)
Construct the Gaussian kernel with a custom bandwidth.
double Normalizer(const size_t dimension)
Obtain the normalization constant of the Gaussian kernel.
double Bandwidth() const
Get the bandwidth.
double Gamma() const
Get the precalculated constant.
void serialize(Archive &ar, const unsigned int)
Serialize the kernel.
double ConvolutionIntegral(const VecTypeA &a, const VecTypeB &b)
Obtain a convolution integral of the Gaussian kernel.
This is a template class that can provide information about various kernels.
static const bool UsesSquaredDistance
If true, then the kernel include a squared distance, ||x - y||^2 .
static const bool IsNormalized
If true, then the kernel is normalized: K(x, x) = K(y, y) = 1 for all x.
static VecTypeA::elem_type Evaluate(const VecTypeA &a, const VecTypeB &b)
Computes the distance between two points.
Linear algebra utility functions, generally performed on matrices or vectors.
The core includes that mlpack expects; standard C++ includes and Armadillo.