A base class for kernel (aka Parzen window) distributions. More...
#include <vpdl_kernel_base.h>
Public Types | |
| typedef vpdt_field_default< T, n >::type | vector |
| the data type used for vectors. | |
| typedef vpdt_field_traits < vector >::matrix_type | matrix |
| the data type used for matrices. | |
| typedef vpdt_field_default< T, n >::type | field_type |
| the data type used for vectors. | |
Public Member Functions | |
| vpdl_kernel_base () | |
| vpdl_kernel_base (const vcl_vector< vector > &samplez) | |
| unsigned int | num_components () const |
| Return the number of components in the mixture. | |
| virtual unsigned int | dimension () const |
Return the run time dimension, which does not equal n when n==0. | |
| virtual void | add_sample (const vector &s) |
| Add a new sample point. | |
| virtual void | clear_samples () |
| Remove all sample points. | |
| virtual void | set_samples (const vcl_vector< vector > &samplez) |
| Set the collection of sample points. | |
| const vcl_vector< vector > & | samples () const |
| Access the sample points. | |
| virtual void | compute_mean (vector &mean) const |
| Compute the mean of the distribution. | |
| virtual vpdl_distribution< T, n > * | clone () const =0 |
| Create a copy on the heap and return base class pointer. | |
| virtual T | density (const vector &pt) const =0 |
| Evaluate the unnormalized density at a point. | |
| virtual T | prob_density (const vector &pt) const |
| Evaluate the probability density at a point. | |
| virtual T | log_prob_density (const vector &pt) const |
| Evaluate the log probability density at a point. | |
| virtual T | gradient_density (const vector &pt, vector &g) const =0 |
| Compute the gradient of the unnormalized density at a point. | |
| virtual T | norm_const () const =0 |
| The normalization constant for the density. | |
| virtual T | cumulative_prob (const vector &pt) const =0 |
| Evaluate the cumulative distribution function at a point. | |
| virtual vector | inverse_cdf (const T &p) const |
| Compute the inverse of the cumulative_prob() function. | |
| virtual T | box_prob (const vector &min_pt, const vector &max_pt) const |
| The probability of being in an axis-aligned box. | |
| virtual void | compute_covar (matrix &covar) const =0 |
| Compute the covariance of the distribution. | |
Private Attributes | |
| vcl_vector< vector > | samples_ |
| The sample points around which the kernels are centered. | |
Detailed Description
template<class T, unsigned int n = 0>
class vpdl_kernel_base< T, n >
A base class for kernel (aka Parzen window) distributions.
A kernel distribution is restricted form of a mixture where each component has the same weight and takes the same form. Essentially, a copy of a single distribution is translated (and possibly scaled) to each point in a collection of samples
Definition at line 26 of file vpdl_kernel_base.h.
Member Typedef Documentation
typedef vpdt_field_default<T,n>::type vpdl_distribution< T, n >::field_type [inherited] |
the data type used for vectors.
Reimplemented in vpdl_mixture_of< dist_t >.
Definition at line 36 of file vpdl_distribution.h.
| typedef vpdt_field_traits<vector>::matrix_type vpdl_kernel_base< T, n >::matrix |
the data type used for matrices.
Reimplemented from vpdl_multi_cmp_dist< T, n >.
Reimplemented in vpdl_kernel_vbw_base< T, n >, vpdl_kernel_fbw_base< T, n >, and vpdl_kernel_gaussian_sfbw< T, n >.
Definition at line 32 of file vpdl_kernel_base.h.
| typedef vpdt_field_default<T,n>::type vpdl_kernel_base< T, n >::vector |
the data type used for vectors.
Reimplemented from vpdl_multi_cmp_dist< T, n >.
Reimplemented in vpdl_kernel_vbw_base< T, n >, vpdl_kernel_fbw_base< T, n >, and vpdl_kernel_gaussian_sfbw< T, n >.
Definition at line 30 of file vpdl_kernel_base.h.
Constructor & Destructor Documentation
| vpdl_kernel_base< T, n >::vpdl_kernel_base | ( | ) | [inline] |
Definition at line 35 of file vpdl_kernel_base.h.
| vpdl_kernel_base< T, n >::vpdl_kernel_base | ( | const vcl_vector< vector > & | samplez | ) | [inline] |
Definition at line 38 of file vpdl_kernel_base.h.
Member Function Documentation
| virtual void vpdl_kernel_base< T, n >::add_sample | ( | const vector & | s | ) | [inline, virtual] |
Add a new sample point.
Reimplemented in vpdl_kernel_vbw_base< T, n >.
Definition at line 53 of file vpdl_kernel_base.h.
| T vpdl_distribution< T, n >::box_prob | ( | const vector & | min_pt, |
| const vector & | max_pt | ||
| ) | const [virtual, inherited] |
The probability of being in an axis-aligned box.
The box is defined by two points, the minimum and maximum. Implemented in terms of cumulative_prob() by default.
Reimplemented in vpdl_mixture< T, n >, vpdl_kernel_gaussian_sfbw< T, n >, vpdl_gaussian_sphere< T, n >, and vpdl_mixture_of< dist_t >.
Definition at line 86 of file vpdl_distribution.txx.
| virtual void vpdl_kernel_base< T, n >::clear_samples | ( | ) | [inline, virtual] |
Remove all sample points.
Reimplemented in vpdl_kernel_vbw_base< T, n >.
Definition at line 61 of file vpdl_kernel_base.h.
| virtual vpdl_distribution<T,n>* vpdl_distribution< T, n >::clone | ( | ) | const [pure virtual, inherited] |
Create a copy on the heap and return base class pointer.
Implemented in vpdl_mixture< T, n >, vpdl_mixture_of< dist_t >, vpdl_gaussian_sphere< T, n >, vpdl_gaussian_indep< T, n >, vpdl_gaussian< T, n >, and vpdl_kernel_gaussian_sfbw< T, n >.
| virtual void vpdl_distribution< T, n >::compute_covar | ( | matrix & | covar | ) | const [pure virtual, inherited] |
Compute the covariance of the distribution.
This may be trivial for distributions like Gaussians, but actually involves computation for others.
Implemented in vpdl_mixture< T, n >, vpdl_kernel_gaussian_sfbw< T, n >, vpdl_gaussian_sphere< T, n >, vpdl_gaussian< T, n >, vpdl_gaussian_indep< T, n >, and vpdl_mixture_of< dist_t >.
| virtual void vpdl_kernel_base< T, n >::compute_mean | ( | vector & | mean | ) | const [inline, virtual] |
Compute the mean of the distribution.
Assume that each kernel has its mean at the sample point
Implements vpdl_distribution< T, n >.
Definition at line 80 of file vpdl_kernel_base.h.
| virtual T vpdl_distribution< T, n >::cumulative_prob | ( | const vector & | pt | ) | const [pure virtual, inherited] |
Evaluate the cumulative distribution function at a point.
This is the integral of the density function from negative infinity (in all dimensions) to the point in question
- Note:
- It is not possible to compute this value for all functions in closed form. In some cases, numerical integration may be used. If no good solutions exists the function should return a quiet NaN.
Implemented in vpdl_mixture< T, n >, vpdl_kernel_gaussian_sfbw< T, n >, vpdl_mixture_of< dist_t >, vpdl_gaussian_sphere< T, n >, vpdl_gaussian_indep< T, n >, and vpdl_gaussian< T, n >.
| virtual T vpdl_distribution< T, n >::density | ( | const vector & | pt | ) | const [pure virtual, inherited] |
Evaluate the unnormalized density at a point.
- Note:
- This is not a probability density. To make this a probability multiply by norm_const()
- See also:
- prob_density
Implemented in vpdl_mixture< T, n >, vpdl_mixture_of< dist_t >, vpdl_gaussian_sphere< T, n >, vpdl_gaussian_indep< T, n >, vpdl_gaussian< T, n >, and vpdl_kernel_gaussian_sfbw< T, n >.
| virtual unsigned int vpdl_kernel_base< T, n >::dimension | ( | ) | const [inline, virtual] |
Return the run time dimension, which does not equal n when n==0.
Implements vpdl_distribution< T, n >.
Definition at line 45 of file vpdl_kernel_base.h.
| virtual T vpdl_distribution< T, n >::gradient_density | ( | const vector & | pt, |
| vector & | g | ||
| ) | const [pure virtual, inherited] |
Compute the gradient of the unnormalized density at a point.
- Returns:
- the density at pt since it is usually needed as well, and is often trivial to compute while computing gradient
- Return values:
-
g the gradient vector
Implemented in vpdl_mixture< T, n >, vpdl_mixture_of< dist_t >, vpdl_kernel_gaussian_sfbw< T, n >, vpdl_gaussian_sphere< T, n >, vpdl_gaussian_indep< T, n >, and vpdl_gaussian< T, n >.
| vpdl_distribution< T, n >::vector vpdl_distribution< T, n >::inverse_cdf | ( | const T & | p | ) | const [virtual, inherited] |
Compute the inverse of the cumulative_prob() function.
The value of x: P(x'<x) = P for x' drawn from the distribution.
- Note:
- This is only valid for univariate distributions multivariate distributions will return a quiet NaN
The value of x: P(x'<x) = P for x' drawn from the distribution. This is only valid for univariate distributions multivariate distributions will return -infinity
Definition at line 75 of file vpdl_distribution.txx.
| virtual T vpdl_distribution< T, n >::log_prob_density | ( | const vector & | pt | ) | const [inline, virtual, inherited] |
Evaluate the log probability density at a point.
Reimplemented in vpdl_gaussian_sphere< T, n >, vpdl_gaussian_indep< T, n >, and vpdl_gaussian< T, n >.
Definition at line 62 of file vpdl_distribution.h.
| virtual T vpdl_distribution< T, n >::norm_const | ( | ) | const [pure virtual, inherited] |
The normalization constant for the density.
When density() is multiplied by this value it becomes prob_density norm_const() is reciprocal of the integral of density over the entire field
Implemented in vpdl_mixture< T, n >, vpdl_kernel_fbw_base< T, n >, vpdl_mixture_of< dist_t >, vpdl_gaussian_sphere< T, n >, vpdl_gaussian_indep< T, n >, and vpdl_gaussian< T, n >.
| unsigned int vpdl_kernel_base< T, n >::num_components | ( | ) | const [inline, virtual] |
Return the number of components in the mixture.
Implements vpdl_multi_cmp_dist< T, n >.
Definition at line 42 of file vpdl_kernel_base.h.
| virtual T vpdl_distribution< T, n >::prob_density | ( | const vector & | pt | ) | const [inline, virtual, inherited] |
Evaluate the probability density at a point.
Reimplemented in vpdl_mixture< T, n >, vpdl_mixture_of< dist_t >, vpdl_kernel_gaussian_sfbw< T, n >, vpdl_gaussian_sphere< T, n >, vpdl_gaussian_indep< T, n >, and vpdl_gaussian< T, n >.
Definition at line 56 of file vpdl_distribution.h.
| const vcl_vector<vector>& vpdl_kernel_base< T, n >::samples | ( | ) | const [inline] |
Access the sample points.
Definition at line 73 of file vpdl_kernel_base.h.
| virtual void vpdl_kernel_base< T, n >::set_samples | ( | const vcl_vector< vector > & | samplez | ) | [inline, virtual] |
Set the collection of sample points.
Reimplemented in vpdl_kernel_vbw_base< T, n >.
Definition at line 67 of file vpdl_kernel_base.h.
Member Data Documentation
vcl_vector<vector> vpdl_kernel_base< T, n >::samples_ [private] |
The sample points around which the kernels are centered.
Definition at line 96 of file vpdl_kernel_base.h.
The documentation for this class was generated from the following file:
- core/vpdl/vpdl_kernel_base.h
