The Epanechnikov kernel, defined as.
More...
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| | EpanechnikovKernel (const double bandwidth=1.0) |
| | Instantiate the Epanechnikov kernel with the given bandwidth (default 1.0). More...
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| 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...
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| template<typename VecTypeA , typename VecTypeB > |
| double | Evaluate (const VecTypeA &a, const VecTypeB &b) const |
| | Evaluate the Epanechnikov kernel on the given two inputs. More...
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| double | Evaluate (const double distance) const |
| | Evaluate the Epanechnikov kernel given that the distance between the two input points is known. More...
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| double | Gradient (const double distance) const |
| | Evaluate the Gradient of Epanechnikov kernel given that the distance between the two input points is known. More...
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| 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...
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| double | Normalizer (const size_t dimension) |
| | Compute the normalizer of this Epanechnikov kernel for the given dimension. More...
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| template<typename Archive > |
| void | serialize (Archive &ar, const unsigned int version) |
| | Serialize the kernel. More...
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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.
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.
| double ConvolutionIntegral |
( |
const VecTypeA & |
a, |
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const VecTypeB & |
b |
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) |
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Obtains the convolution integral [integral of K(||x-a||) K(||b-x||) dx] for the two vectors.
- Template Parameters
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| VecType | Type of vector (arma::vec, arma::spvec should be expected). |
- Parameters
-
| a | First vector. |
| b | Second vector. |
- Returns
- the convolution integral value.
| double Evaluate |
( |
const VecTypeA & |
a, |
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const VecTypeB & |
b |
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) |
| const |
Evaluate the Epanechnikov kernel on the given two inputs.
- Template Parameters
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| VecTypeA | Type of first vector. |
| VecTypeB | Type of second vector. |
- Parameters
-
| a | One input vector. |
| b | The other input vector. |
| double Evaluate |
( |
const double |
distance | ) |
const |
Evaluate the Epanechnikov kernel given that the distance between the two input points is known.
| double Gradient |
( |
const double |
distance | ) |
const |
Evaluate the Gradient of Epanechnikov kernel given that the distance between the two input points is known.
| double GradientForSquaredDistance |
( |
const double |
distanceSquared | ) |
const |
Evaluate the Gradient of Epanechnikov kernel given that the squared distance between the two input points is known.
| double Normalizer |
( |
const size_t |
dimension | ) |
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Compute the normalizer of this Epanechnikov kernel for the given dimension.
- Parameters
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| dimension | Dimension to calculate the normalizer for. |
| void serialize |
( |
Archive & |
ar, |
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const unsigned int |
version |
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) |
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The documentation for this class was generated from the following file:
1.8.5