Truncated Fourier feature map using log-sized intervals between each interval of the normal distribution, from the origin to 3 standard deviations on each side. More...

#include <LogTruncatedFourierFeatureMap.h>

Inheritance diagram for lucid::LogTruncatedFourierFeatureMap:

Public Member Functions
std::unique_ptr< FeatureMap >	clone () const override
	Clone the feature map.

std::string	to_string () const override
	Obtain the string representation of this object.

Public Member Functions inherited from lucid::TruncatedFourierFeatureMap
	TruncatedFourierFeatureMap (int num_frequencies, const Matrix &prob_per_dim, const Matrix &omega_per_dim, ConstVectorRef sigma_l, Scalar sigma_f, const RectSet &X_bounds)
	Construct a truncated Fourier feature map.

	TruncatedFourierFeatureMap (int num_frequencies, const Matrix &prob_per_dim, const Matrix &omega_per_dim, double sigma_l, Scalar sigma_f, const RectSet &X_bounds)
	Construct a truncated Fourier feature map.

Vector	map_vector (ConstVectorRef x) const
	Given a \( \texttip{d}{Dimension of the vector space} \) dimensional vector \( \texttip{x}{Element of the vector space} \), project it to the unit hypercube \( [0, 1]^d \), then compute the feature map.

Vector	invert_vector (ConstVectorRef y) const
	Given a @2M+1 dimensional vector \( \texttip{y}{Element of the vector space} \), invert the feature map to obtain the original input vector.

Matrix	map_matrix (ConstMatrixRef x) const
	Given an \( \texttip{n}{Number of samples} \times \texttip{d}{Dimension of the vector space} \) dimensional matrix \( \texttip{x}{Element of the vector space} \), project each row vector to the unit hypercube \( [0, 1]^d \), then compute the feature map.

Dimension	dimension () const
	Get read-only access to the dimension of the the feature map space.

const Matrix &	omega () const
	Get read-only access to the frequency matrix of the truncated Fourier feature map.

const Vector &	weights () const
	Get read-only access to the weights matrix of the truncated Fourier feature map.

int	num_frequencies () const
	Get read-only access to the number of frequencies per dimension of the truncated Fourier feature map.

Scalar	captured_probability () const
	Get read-only access to the probability captured by the Fourier expansion of the truncated Fourier feature map.

const RectSet &	X_bounds () const
	Get read-only access to the limits of the original input space.

double	sigma_f () const
	Get read-only access to the sigma_f value of the truncated Fourier feature map.

const Vector &	sigma_l () const
	Get read-only access to the sigma_l value of the truncated Fourier feature map.

virtual RectSet	get_periodic_set () const
	Return the periodic input domain for this linear truncated Fourier map.

std::unique_ptr< FeatureMap >	clone () const override
	Clone the feature map.

Public Member Functions inherited from lucid::FeatureMap
Matrix	operator() (ConstMatrixRef x) const
	Apply the feature map to a vector.

Matrix	invert (ConstMatrixRef y) const
	Apply the inverse feature map to a vector.

Additional Inherited Members
Protected Member Functions inherited from lucid::TruncatedFourierFeatureMap
Matrix	apply_impl (ConstMatrixRef x) const override
	Given an \( \texttip{n}{Number of samples} \times \texttip{d}{Dimension of the vector space} \) dimensional matrix \( \texttip{x}{Element of the vector space} \), project each row vector to the unit hypercube \( [0, 1]^d \), then compute the feature map.

Matrix	invert_impl (ConstMatrixRef y) const override
	Concrete implementation of invert().

Protected Attributes inherited from lucid::TruncatedFourierFeatureMap
int	num_frequencies_
	Number of frequencies per dimension.

Matrix	omega_
	Frequencies matrix.

Vector	weights_
	Weights matrix.

Scalar	sigma_f_
	\( \sigma_f \) value

Vector	sigma_l_
	\( \sigma_l \) vector

RectSet	X_bounds_
	Limits of the input space expressed as a matrix. The set is a rectangle.

Scalar	captured_probability_
	Probability captured by the Fourier expansion. NaN if not computed.

Detailed Description

Truncated Fourier feature map using log-sized intervals between each interval of the normal distribution, from the origin to 3 standard deviations on each side.

The weights are computed from the n-dimensional cumulative distribution function of the normal distribution with standard deviation \( \sigma_l \), i.e.

\[ w_j^2 := \int_{(2\hat{\zeta}_j-1)\pi}^{(2\hat{\zeta}_j+1)\pi}\mathcal{N}(d\xi|0,\Sigma), 1 \le j \le M . \]

where \( \hat{\zeta}_j \) is a transformation of the original \( \zeta_j \).