mlpack::radical::Radical Class Reference

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

#include <radical.hpp>

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. More...
void	DoRadical (const arma::mat &matX, arma::mat &matY, arma::mat &matW)
	Run RADICAL. More...
double	Vasicek (arma::vec &x) const
	Vasicek's m-spacing estimator of entropy, with overlap modification from (Learned-Miller and Fisher, 2003). More...
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.
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	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.
size_t	Sweeps () const
	Get the number of sweeps.
size_t &	Sweeps ()
	Modify the number of sweeps.

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}
}

Constructor & Destructor Documentation

Radical()

Radical::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.

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

DoRadical()

void 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.

Vasicek()

double 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.

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

• src/mlpack/methods/radical/radical.hpp
• src/mlpack/methods/radical/radical.cpp