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 (
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>
void Serialize(Archive &ar, const unsigned int)
Serialize the kernel.
This is a template class that can provide information about various kernels.
double Gradient(const double t) const
Evaluation of the gradient of Gaussian kernel given the distance between two points.
FirstShim< T > CreateNVP(T &t, const std::string &name, typename boost::enable_if< HasSerialize< T >>::type *=0)
Call this function to produce a name-value pair; this is similar to BOOST_SERIALIZATION_NVP(), but should be used for types that have a Serialize() function (or contain a type that has a Serialize() function) instead of a serialize() function.
double Gamma() const
Get the precalculated constant.
The core includes that mlpack expects; standard C++ includes and Armadillo.
static VecTypeA::elem_type Evaluate(const VecTypeA &a, const VecTypeB &b)
Computes the distance between two points.
GaussianKernel(const double bandwidth)
Construct the Gaussian kernel with a custom bandwidth.
double GradientForSquaredDistance(const double t) const
Evaluation of the gradient of Gaussian kernel given the squared distance between two points...
GaussianKernel()
Default constructor; sets bandwidth to 1.0.
double Bandwidth() const
Get the bandwidth.
double Evaluate(const double t) const
Evaluation of the Gaussian kernel given the distance between two points.
double ConvolutionIntegral(const VecTypeA &a, const VecTypeB &b)
Obtain a convolution integral of the Gaussian kernel.
static const bool IsNormalized
If true, then the kernel is normalized: K(x, x) = K(y, y) = 1 for all x.
The standard Gaussian kernel.
double Evaluate(const VecTypeA &a, const VecTypeB &b) const
Evaluation of the Gaussian kernel.
void Bandwidth(const double bandwidth)
Modify the bandwidth.
double Normalizer(const size_t dimension)
Obtain the normalization constant of the Gaussian kernel.
static const bool UsesSquaredDistance
If true, then the kernel include a squared distance, ||x - y||^2 .