The Epanechnikov kernel, defined as. More...
Public Member Functions | |
| EpanechnikovKernel (const double bandwidth=1.0) | |
| Instantiate the Epanechnikov kernel with the given bandwidth (default 1.0). More... | |
template < typename VecTypeA , typename VecTypeB > | |
| 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. More... | |
template < typename VecTypeA , typename VecTypeB > | |
| double | Evaluate (const VecTypeA &a, const VecTypeB &b) const |
| Evaluate the Epanechnikov kernel on the given two inputs. More... | |
| double | Evaluate (const double distance) const |
| Evaluate the Epanechnikov kernel given that the distance between the two input points is known. More... | |
| double | Gradient (const double distance) const |
| Evaluate the Gradient of Epanechnikov kernel given that the distance between the two input points is known. More... | |
| double | GradientForSquaredDistance (const double distanceSquared) const |
| Evaluate the Gradient of Epanechnikov kernel given that the squared distance between the two input points is known. More... | |
| double | Normalizer (const size_t dimension) |
| Compute the normalizer of this Epanechnikov kernel for the given dimension. More... | |
template < typename Archive > | |
| void | serialize (Archive &ar, const uint32_t version) |
| Serialize the kernel. More... | |
Detailed Description
The Epanechnikov kernel, defined as.
![\[ K(x, y) = \max \{0, 1 - || x - y ||^2_2 / b^2 \} \]](form_41.png)
where 
is the bandwidth the of the kernel (defaults to 1.0).
Definition at line 30 of file epanechnikov_kernel.hpp.
Constructor & Destructor Documentation
◆ EpanechnikovKernel()
|
inline |
Instantiate the Epanechnikov kernel with the given bandwidth (default 1.0).
- Parameters
-
bandwidth Bandwidth of the kernel.
Definition at line 38 of file epanechnikov_kernel.hpp.
References EpanechnikovKernel::ConvolutionIntegral(), EpanechnikovKernel::Evaluate(), EpanechnikovKernel::Gradient(), EpanechnikovKernel::GradientForSquaredDistance(), EpanechnikovKernel::Normalizer(), and EpanechnikovKernel::serialize().
Member Function Documentation
◆ ConvolutionIntegral()
| 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.
- Template Parameters
-
VecType Type of vector (arma::vec, arma::spvec should be expected).
- Parameters
-
a First vector. b Second vector.
- Returns
- the convolution integral value.
Referenced by EpanechnikovKernel::EpanechnikovKernel().
◆ Evaluate() [1/2]
| double Evaluate | ( | const VecTypeA & | a, |
| const VecTypeB & | b | ||
| ) | const |
Evaluate the Epanechnikov kernel on the given two inputs.
- Template Parameters
-
VecTypeA Type of first vector. VecTypeB Type of second vector.
- Parameters
-
a One input vector. b The other input vector.
Referenced by EpanechnikovKernel::EpanechnikovKernel().
◆ Evaluate() [2/2]
| double Evaluate | ( | const double | distance | ) | const |
Evaluate the Epanechnikov kernel given that the distance between the two input points is known.
◆ Gradient()
| double Gradient | ( | const double | distance | ) | const |
Evaluate the Gradient of Epanechnikov kernel given that the distance between the two input points is known.
Referenced by EpanechnikovKernel::EpanechnikovKernel().
◆ GradientForSquaredDistance()
| double GradientForSquaredDistance | ( | const double | distanceSquared | ) | const |
Evaluate the Gradient of Epanechnikov kernel given that the squared distance between the two input points is known.
Referenced by EpanechnikovKernel::EpanechnikovKernel().
◆ Normalizer()
| double Normalizer | ( | const size_t | dimension | ) |
Compute the normalizer of this Epanechnikov kernel for the given dimension.
- Parameters
-
dimension Dimension to calculate the normalizer for.
Referenced by EpanechnikovKernel::EpanechnikovKernel().
◆ serialize()
| void serialize | ( | Archive & | ar, |
| const uint32_t | version | ||
| ) |
Serialize the kernel.
Referenced by EpanechnikovKernel::EpanechnikovKernel().
The documentation for this class was generated from the following file:
- /home/ryan/src/mlpack.org/_src/mlpack-git/src/mlpack/core/kernels/epanechnikov_kernel.hpp