SYNOPSIS

Public Member Functions

Radical (const double noiseStdDev=0.175, const size_t replicates=30, const size_t angles=150, const size_t sweeps=0, const size_t m=0)
Set the parameters to RADICAL.
size_t Angles () const
Get the number of angles considered during brute-force search.
size_t & Angles ()
Modify the number of angles considered during brute-force search.
void CopyAndPerturb (arma::mat &xNew, const arma::mat &x) const
Make replicates of each data point (the number of replicates is set in either the constructor or with Replicates()) and perturb data with Gaussian noise with standard deviation noiseStdDev.
void DoRadical (const arma::mat &matX, arma::mat &matY, arma::mat &matW)
Run RADICAL.
double DoRadical2D (const arma::mat &matX)
Two-dimensional version of RADICAL.
double NoiseStdDev () const
Get the standard deviation of the additive Gaussian noise.
double & NoiseStdDev ()
Modify the standard deviation of the additive Gaussian noise.
size_t Replicates () const
Get the number of Gaussian-perturbed replicates used per point.
size_t & Replicates ()
Modify the number of Gaussian-perturbed replicates used per point.
size_t Sweeps () const
Get the number of sweeps.
size_t & Sweeps ()
Modify the number of sweeps.
std::string ToString () const

double Vasicek (arma::vec &x) const
Vasicek's m-spacing estimator of entropy, with overlap modification from (Learned-Miller and Fisher, 2003).

Private Attributes

size_t angles
Number of angles to consider in brute-force search during Radical2D.
arma::mat candidate
Internal matrix, held as member variable to prevent memory reallocations.
size_t m
Value of m to use for Vasicek's m-spacing estimator of entropy.
double noiseStdDev
Standard deviation of the Gaussian noise added to the replicates of the data points during Radical2D.
arma::mat perturbed
Internal matrix, held as member variable to prevent memory reallocations.
size_t replicates
Number of Gaussian-perturbed replicates to use (per point) in Radical2D.
size_t sweeps
Number of sweeps; each sweep calls Radical2D once for each pair of dimensions.

Detailed Description

An implementation of RADICAL, an algorithm for independent component analysis (ICA).

Let X be a matrix where each column is a point and each row a dimension. The goal is to find a square unmixing matrix W such that Y = W X and the rows of Y are independent components.

For more details, see the following paper:

@article{learned2003ica,
  title = {ICA Using Spacings Estimates of Entropy},
  author = {Learned-Miller, E.G. and Fisher III, J.W.},
  journal = {Journal of Machine Learning Research},
  volume = {4},
  pages = {1271--1295},
  year = {2003}
}

Definition at line 53 of file radical.hpp.

Constructor & Destructor Documentation

mlpack::radical::Radical::Radical (const doublenoiseStdDev = 0.175, const size_treplicates = 30, const size_tangles = 150, const size_tsweeps = 0, const size_tm = 0)

Set the parameters to RADICAL.

Parameters:

noiseStdDev Standard deviation of the Gaussian noise added to the replicates of the data points during Radical2D
replicates Number of Gaussian-perturbed replicates to use (per point) in Radical2D
angles Number of angles to consider in brute-force search during Radical2D
sweeps Number of sweeps. Each sweep calls Radical2D once for each pair of dimensions
m The variable m from Vasicek's m-spacing estimator of entropy.

Member Function Documentation

size_t mlpack::radical::Radical::Angles () const [inline]

Get the number of angles considered during brute-force search.

Definition at line 115 of file radical.hpp.

References angles.

size_t& mlpack::radical::Radical::Angles () [inline]

Modify the number of angles considered during brute-force search.

Definition at line 117 of file radical.hpp.

References angles.

void mlpack::radical::Radical::CopyAndPerturb (arma::mat &xNew, const arma::mat &x) const

Make replicates of each data point (the number of replicates is set in either the constructor or with Replicates()) and perturb data with Gaussian noise with standard deviation noiseStdDev.

void mlpack::radical::Radical::DoRadical (const arma::mat &matX, arma::mat &matY, arma::mat &matW)

Run RADICAL.

Parameters:

matX Input data into the algorithm - a matrix where each column is a point and each row is a dimension.
matY Estimated independent components - a matrix where each column is a point and each row is an estimated independent component.
matW Estimated unmixing matrix, where matY = matW * matX.

double mlpack::radical::Radical::DoRadical2D (const arma::mat &matX)

Two-dimensional version of RADICAL.

double mlpack::radical::Radical::NoiseStdDev () const [inline]

Get the standard deviation of the additive Gaussian noise.

Definition at line 105 of file radical.hpp.

References noiseStdDev.

double& mlpack::radical::Radical::NoiseStdDev () [inline]

Modify the standard deviation of the additive Gaussian noise.

Definition at line 107 of file radical.hpp.

References noiseStdDev.

size_t mlpack::radical::Radical::Replicates () const [inline]

Get the number of Gaussian-perturbed replicates used per point.

Definition at line 110 of file radical.hpp.

References replicates.

size_t& mlpack::radical::Radical::Replicates () [inline]

Modify the number of Gaussian-perturbed replicates used per point.

Definition at line 112 of file radical.hpp.

References replicates.

size_t mlpack::radical::Radical::Sweeps () const [inline]

Get the number of sweeps.

Definition at line 120 of file radical.hpp.

References sweeps.

size_t& mlpack::radical::Radical::Sweeps () [inline]

Modify the number of sweeps.

Definition at line 122 of file radical.hpp.

References sweeps.

std::string mlpack::radical::Radical::ToString () const

double mlpack::radical::Radical::Vasicek (arma::vec &x) const

Vasicek's m-spacing estimator of entropy, with overlap modification from (Learned-Miller and Fisher, 2003).

Parameters:

x Empirical sample (one-dimensional) over which to estimate entropy.

Member Data Documentation

size_t mlpack::radical::Radical::angles [private]

Number of angles to consider in brute-force search during Radical2D.

Definition at line 136 of file radical.hpp.

Referenced by Angles().

arma::mat mlpack::radical::Radical::candidate [private]

Internal matrix, held as member variable to prevent memory reallocations.

Definition at line 148 of file radical.hpp.

size_t mlpack::radical::Radical::m [private]

Value of m to use for Vasicek's m-spacing estimator of entropy.

Definition at line 143 of file radical.hpp.

double mlpack::radical::Radical::noiseStdDev [private]

Standard deviation of the Gaussian noise added to the replicates of the data points during Radical2D.

Definition at line 130 of file radical.hpp.

Referenced by NoiseStdDev().

arma::mat mlpack::radical::Radical::perturbed [private]

Internal matrix, held as member variable to prevent memory reallocations.

Definition at line 146 of file radical.hpp.

size_t mlpack::radical::Radical::replicates [private]

Number of Gaussian-perturbed replicates to use (per point) in Radical2D.

Definition at line 133 of file radical.hpp.

Referenced by Replicates().

size_t mlpack::radical::Radical::sweeps [private]

Number of sweeps; each sweep calls Radical2D once for each pair of dimensions.

Definition at line 140 of file radical.hpp.

Referenced by Sweeps().

Author

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