A base class for kernel (aka Parzen window) distributions. More...

#include <vpdl_kernel_base.h>

Inheritance diagram for vpdl_kernel_base< T, n >:

[legend]

Public Types
typedef vpdt_field_default< T, n >::type	vector
	the data type used for vectors. More...

typedef vpdt_field_traits< vector >::matrix_type	matrix
	the data type used for matrices. More...

typedef vpdt_field_default< T, n >::type	field_type
	the data type used for vectors. More...

Public Member Functions
	vpdl_kernel_base ()

	vpdl_kernel_base (const std::vector< vector > &samplez)

unsigned int	num_components () const
	Return the number of components in the mixture. More...

virtual unsigned int	dimension () const
	Return the run time dimension, which does not equal `n` when `n==0`. More...

virtual void	add_sample (const vector &s)
	Add a new sample point. More...

virtual void	clear_samples ()
	Remove all sample points. More...

virtual void	set_samples (const std::vector< vector > &samplez)
	Set the collection of sample points. More...

const std::vector< vector > &	samples () const
	Access the sample points. More...

virtual void	compute_mean (vector &mean) const
	Compute the mean of the distribution. More...

virtual vpdl_distribution< T, n > *	clone () const =0
	Create a copy on the heap and return base class pointer. More...

virtual T	density (const vector &pt) const =0
	Evaluate the unnormalized density at a point. More...

virtual T	prob_density (const vector &pt) const
	Evaluate the probability density at a point. More...

virtual T	log_prob_density (const vector &pt) const
	Evaluate the log probability density at a point. More...

virtual T	gradient_density (const vector &pt, vector &g) const =0
	Compute the gradient of the unnormalized density at a point. More...

virtual T	norm_const () const =0
	The normalization constant for the density. More...

virtual T	cumulative_prob (const vector &pt) const =0
	Evaluate the cumulative distribution function at a point. More...

virtual vector	inverse_cdf (const T &p) const
	Compute the inverse of the cumulative_prob() function. More...

virtual T	box_prob (const vector &min_pt, const vector &max_pt) const
	The probability of being in an axis-aligned box. More...

virtual void	compute_covar (matrix &covar) const =0
	Compute the covariance of the distribution. More...

Private Attributes
std::vector< vector >	samples_
	The sample points around which the kernels are centered. More...

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 29 of file vpdl_kernel_base.h.

Member Typedef Documentation

◆ field_type

template<class T, unsigned int n = 0>

typedef vpdt_field_default<T,n>::type vpdl_distribution< T, n >::field_type

inherited

the data type used for vectors.

Definition at line 39 of file vpdl_distribution.h.

◆ matrix

template<class T , unsigned int n = 0>

typedef vpdt_field_traits<vector>::matrix_type vpdl_kernel_base< T, n >::matrix

the data type used for matrices.

Definition at line 35 of file vpdl_kernel_base.h.

◆ vector

template<class T , unsigned int n = 0>

typedef vpdt_field_default<T,n>::type vpdl_kernel_base< T, n >::vector

the data type used for vectors.

Definition at line 33 of file vpdl_kernel_base.h.

Constructor & Destructor Documentation

◆ vpdl_kernel_base() [1/2]

template<class T , unsigned int n = 0>

vpdl_kernel_base< T, n >::vpdl_kernel_base ( )

inline

Definition at line 38 of file vpdl_kernel_base.h.

◆ vpdl_kernel_base() [2/2]

template<class T , unsigned int n = 0>

vpdl_kernel_base< T, n >::vpdl_kernel_base ( const std::vector< vector > & samplez )

inline

Definition at line 41 of file vpdl_kernel_base.h.

Member Function Documentation

◆ add_sample()

template<class T , unsigned int n = 0>

virtual void vpdl_kernel_base< T, n >::add_sample ( const vector & s )

inlinevirtual

Add a new sample point.

Reimplemented in vpdl_kernel_vbw_base< T, n >.

Definition at line 56 of file vpdl_kernel_base.h.

◆ box_prob()

template<class T , unsigned int n>

T vpdl_distribution< T, n >::box_prob	(	const vector &	min_pt,
		const vector &	max_pt
	)		const

virtualinherited

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 >, and vpdl_gaussian_sphere< T, n >.

Definition at line 89 of file vpdl_distribution.hxx.

◆ clear_samples()

template<class T , unsigned int n = 0>

virtual void vpdl_kernel_base< T, n >::clear_samples ( )

inlinevirtual

Remove all sample points.

Reimplemented in vpdl_kernel_vbw_base< T, n >.

Definition at line 64 of file vpdl_kernel_base.h.

◆ clone()

template<class T, unsigned int n = 0>

virtual vpdl_distribution<T,n>* vpdl_distribution< T, n >::clone ( ) const

pure virtualinherited

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 >.

◆ compute_covar()

template<class T, unsigned int n = 0>

virtual void vpdl_distribution< T, n >::compute_covar ( matrix & covar ) const

pure virtualinherited

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 >.

◆ compute_mean()

template<class T , unsigned int n = 0>

virtual void vpdl_kernel_base< T, n >::compute_mean ( vector & mean ) const

inlinevirtual

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 83 of file vpdl_kernel_base.h.

◆ cumulative_prob()

template<class T, unsigned int n = 0>

virtual T vpdl_distribution< T, n >::cumulative_prob ( const vector & pt ) const

pure virtualinherited

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_gaussian_sphere< T, n >, vpdl_gaussian_indep< T, n >, and vpdl_gaussian< T, n >.

◆ density()

template<class T, unsigned int n = 0>

virtual T vpdl_distribution< T, n >::density ( const vector & pt ) const

pure virtualinherited

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_gaussian_sphere< T, n >, vpdl_gaussian_indep< T, n >, vpdl_gaussian< T, n >, and vpdl_kernel_gaussian_sfbw< T, n >.

◆ dimension()

template<class T , unsigned int n = 0>

virtual unsigned int vpdl_kernel_base< T, n >::dimension ( ) const

inlinevirtual

Return the run time dimension, which does not equal n when n==0.

Implements vpdl_distribution< T, n >.

Definition at line 48 of file vpdl_kernel_base.h.

◆ gradient_density()

template<class T, unsigned int n = 0>

virtual T vpdl_distribution< T, n >::gradient_density	(	const vector &	pt,
		vector &	g
	)		const

pure virtualinherited

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_kernel_gaussian_sfbw< T, n >, vpdl_gaussian_sphere< T, n >, vpdl_gaussian_indep< T, n >, and vpdl_gaussian< T, n >.

◆ inverse_cdf()

template<class T, unsigned int n>

vpdl_distribution< T, n >::vector vpdl_distribution< T, n >::inverse_cdf ( const T & p ) const

virtualinherited

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 78 of file vpdl_distribution.hxx.

◆ log_prob_density()

template<class T, unsigned int n = 0>

virtual T vpdl_distribution< T, n >::log_prob_density ( const vector & pt ) const

inlinevirtualinherited

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 65 of file vpdl_distribution.h.

◆ norm_const()

template<class T, unsigned int n = 0>

virtual T vpdl_distribution< T, n >::norm_const ( ) const

pure virtualinherited

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 >.

◆ num_components()

template<class T , unsigned int n = 0>

unsigned int vpdl_kernel_base< T, n >::num_components ( ) const

inlinevirtual

Return the number of components in the mixture.

Implements vpdl_multi_cmp_dist< T, n >.

Definition at line 45 of file vpdl_kernel_base.h.

◆ prob_density()

template<class T, unsigned int n = 0>

virtual T vpdl_distribution< T, n >::prob_density ( const vector & pt ) const

inlinevirtualinherited

Evaluate the probability density at a point.

Reimplemented in vpdl_mixture< T, n >, vpdl_kernel_gaussian_sfbw< T, n >, vpdl_gaussian_sphere< T, n >, vpdl_gaussian_indep< T, n >, and vpdl_gaussian< T, n >.

Definition at line 59 of file vpdl_distribution.h.

◆ samples()

template<class T , unsigned int n = 0>

const std::vector<vector>& vpdl_kernel_base< T, n >::samples ( ) const

inline

Access the sample points.

Definition at line 76 of file vpdl_kernel_base.h.

◆ set_samples()

template<class T , unsigned int n = 0>

virtual void vpdl_kernel_base< T, n >::set_samples ( const std::vector< vector > & samplez )

inlinevirtual

Set the collection of sample points.

Reimplemented in vpdl_kernel_vbw_base< T, n >.

Definition at line 70 of file vpdl_kernel_base.h.

Member Data Documentation

◆ samples_

template<class T , unsigned int n = 0>

std::vector<vector> vpdl_kernel_base< T, n >::samples_

private

The sample points around which the kernels are centered.

Definition at line 99 of file vpdl_kernel_base.h.

The documentation for this class was generated from the following file:

core/vpdl/vpdl_kernel_base.h

Public Types

Public Member Functions

Private Attributes

Detailed Description

template<class T, unsigned int n = 0> class vpdl_kernel_base< T, n >

Member Typedef Documentation

◆ field_type

◆ matrix

◆ vector

Constructor & Destructor Documentation

◆ vpdl_kernel_base() [1/2]

◆ vpdl_kernel_base() [2/2]

Member Function Documentation

◆ add_sample()

◆ box_prob()

◆ clear_samples()

◆ clone()

◆ compute_covar()

◆ compute_mean()

◆ cumulative_prob()

◆ density()

◆ dimension()

◆ gradient_density()

◆ inverse_cdf()

◆ log_prob_density()

◆ norm_const()

◆ num_components()

◆ prob_density()

◆ samples()

◆ set_samples()

Member Data Documentation

◆ samples_

template<class T, unsigned int n = 0>
class vpdl_kernel_base< T, n >