Randomized SVD is a matrix factorization that is based on randomized matrix approximation techniques, developed in in "Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions". More...

Public Member Functions
	RandomizedSVD (const arma::mat &data, arma::mat &u, arma::vec &s, arma::mat &v, const size_t iteratedPower=0, const size_t maxIterations=2, const size_t rank=0, const double eps=1e-7)
	Create object for the randomized SVD method. More...

	RandomizedSVD (const size_t iteratedPower=0, const size_t maxIterations=2, const double eps=1e-7)
	Create object for the randomized SVD method. More...

void	Apply (const arma::mat &data, arma::mat &u, arma::vec &s, arma::mat &v, const size_t rank)
	Apply Principal Component Analysis to the provided data set using the randomized SVD. More...

double	Epsilon () const
	Get the value used for decomposition stability. More...

double &	Epsilon ()
	Modify the value used for decomposition stability. More...

size_t	IteratedPower () const
	Get the size of the normalized power iterations. More...

size_t &	IteratedPower ()
	Modify the size of the normalized power iterations. More...

size_t	MaxIterations () const
	Get the number of iterations for the power method. More...

size_t &	MaxIterations ()
	Modify the number of iterations for the power method. More...

Private Attributes
double	eps
	The value used for numerical stability. More...

size_t	iteratedPower
	Locally stored size of the normalized power iterations. More...

size_t	maxIterations
	Locally stored number of iterations for the power method. More...

Detailed Description

Randomized SVD is a matrix factorization that is based on randomized matrix approximation techniques, developed in in "Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions".

For more information, see the following.

@article{Halko2011,
  author  = {Halko, N. and Martinsson, P. G. and Tropp, J. A.},
  title   = {Finding Structure with Randomness: Probabilistic Algorithms for
             Constructing Approximate Matrix Decompositions},
  journal = {SIAM Rev.},
  volume  = {53},
  year    = {2011},
}

@article{Szlam2014,
  author  = {Arthur Szlam Yuval Kluger and Mark Tygert},
  title   = {An implementation of a randomized algorithm for principal
             component analysis},
  journal = {CoRR},
  volume  = {abs/1412.3510},
  year    = {2014},
}

An example of how to use the interface is shown below:

arma::mat data; // Rating data in the form of coordinate list.
const size_t rank = 20; // Rank used for the decomposition.
// Make a RandomizedSVD object.
RandomizedSVD rSVD();
arma::mat u, s, v;
// Use the Apply() method to get a factorization.
rSVD.Apply(data, u, s, v, rank);

Definition at line 66 of file randomized_svd.hpp.

Constructor & Destructor Documentation

mlpack::svd::RandomizedSVD::RandomizedSVD	(	const arma::mat &	data,
		arma::mat &	u,
		arma::vec &	s,
		arma::mat &	v,
		const size_t	iteratedPower = `0`,
		const size_t	maxIterations = `2`,
		const size_t	rank = `0`,
		const double	eps = `1e-7`
	)

Create object for the randomized SVD method.

Parameters

data	Data matrix.
u	First unitary matrix.
v	Second unitary matrix.
sigma	Diagonal matrix of singular values.
iteratedPower	Size of the normalized power iterations (Default: rank + 2).
maxIterations	Number of iterations for the power method (Default: 2).
rank	Rank of the approximation (Default: number of rows.)
eps	The eps coefficient to avoid division by zero (numerical stability).

mlpack::svd::RandomizedSVD::RandomizedSVD	(	const size_t	iteratedPower = `0`,
		const size_t	maxIterations = `2`,
		const double	eps = `1e-7`
	)

Create object for the randomized SVD method.

Parameters

iteratedPower	Size of the normalized power iterations (Default: rank + 2).
maxIterations	Number of iterations for the power method (Default: 2).
eps	The eps coefficient to avoid division by zero (numerical stability).

Member Function Documentation

void mlpack::svd::RandomizedSVD::Apply	(	const arma::mat &	data,
		arma::mat &	u,
		arma::vec &	s,
		arma::mat &	v,
		const size_t	rank
	)

Apply Principal Component Analysis to the provided data set using the randomized SVD.

Parameters

data	Data matrix.
u	First unitary matrix.
v	Second unitary matrix.
sigma	Diagonal matrix of singular values.
rank	Rank of the approximation.

Referenced by mlpack::pca::RandomizedSVDPolicy::Apply().

double mlpack::svd::RandomizedSVD::Epsilon ( ) const

inline

Get the value used for decomposition stability.

Definition at line 134 of file randomized_svd.hpp.

References eps.

double& mlpack::svd::RandomizedSVD::Epsilon ( )

inline

Modify the value used for decomposition stability.

Definition at line 136 of file randomized_svd.hpp.

References eps.

size_t mlpack::svd::RandomizedSVD::IteratedPower ( ) const

inline

Get the size of the normalized power iterations.

Definition at line 124 of file randomized_svd.hpp.

References iteratedPower.

size_t& mlpack::svd::RandomizedSVD::IteratedPower ( )

inline

Modify the size of the normalized power iterations.

Definition at line 126 of file randomized_svd.hpp.

References iteratedPower.

size_t mlpack::svd::RandomizedSVD::MaxIterations ( ) const

inline

Get the number of iterations for the power method.

Definition at line 129 of file randomized_svd.hpp.

References maxIterations.

size_t& mlpack::svd::RandomizedSVD::MaxIterations ( )

inline

Modify the number of iterations for the power method.

Definition at line 131 of file randomized_svd.hpp.

References maxIterations.

Member Data Documentation

double mlpack::svd::RandomizedSVD::eps

private

The value used for numerical stability.

Definition at line 146 of file randomized_svd.hpp.

Referenced by Epsilon().

size_t mlpack::svd::RandomizedSVD::iteratedPower

private

Locally stored size of the normalized power iterations.

Definition at line 140 of file randomized_svd.hpp.

Referenced by IteratedPower().

size_t mlpack::svd::RandomizedSVD::maxIterations

private

Locally stored number of iterations for the power method.

Definition at line 143 of file randomized_svd.hpp.

Referenced by MaxIterations().

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

src/mlpack/methods/randomized_svd/randomized_svd.hpp

Public Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation