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::sp_mat &data, arma::mat &u, arma::vec &s, arma::mat &v, const size_t rank)
	Center the data to apply Principal Component Analysis on given sparse matrix dataset using randomized SVD. More...

void	Apply (const arma::mat &data, arma::mat &u, arma::vec &s, arma::mat &v, const size_t rank)
	Center the data to apply Principal Component Analysis on given matrix dataset using randomized SVD. More...

template < typename MatType >
void	Apply (const MatType &data, arma::mat &u, arma::vec &s, arma::mat &v, const size_t rank, MatType rowMean)
	Apply Principal Component Analysis to the provided matrix 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...

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

◆ RandomizedSVD() [1/2]

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.
s	Diagonal "Sigma" 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).

◆ RandomizedSVD() [2/2]

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

◆ Apply() [1/3]

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

Center the data to apply Principal Component Analysis on given sparse matrix dataset using randomized SVD.

Parameters

data	Sparse data matrix.
u	First unitary matrix.
v	Second unitary matrix.
s	Diagonal "Sigma" matrix of singular values.
rank	Rank of the approximation.

Referenced by RandomizedSVDPolicy::Apply().

◆ Apply() [2/3]

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

Center the data to apply Principal Component Analysis on given matrix dataset using randomized SVD.

Parameters

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

◆ Apply() [3/3]

void Apply	(	const MatType &	data,
		arma::mat &	u,
		arma::vec &	s,
		arma::mat &	v,
		const size_t	rank,
		MatType	rowMean
	)

inline

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

Parameters

data	Data matrix.
u	First unitary matrix.
v	Second unitary matrix.
s	Diagonal "Sigma" matrix of singular values.
rank	Rank of the approximation.
rowMean	Centered mean value matrix.

Definition at line 151 of file randomized_svd.hpp.

◆ Epsilon() [1/2]

double Epsilon ( ) const

inline

Get the value used for decomposition stability.

Definition at line 245 of file randomized_svd.hpp.

◆ Epsilon() [2/2]

double& Epsilon ( )

inline

Modify the value used for decomposition stability.

Definition at line 247 of file randomized_svd.hpp.

◆ IteratedPower() [1/2]

size_t IteratedPower ( ) const

inline

Get the size of the normalized power iterations.

Definition at line 235 of file randomized_svd.hpp.

◆ IteratedPower() [2/2]

size_t& IteratedPower ( )

inline

Modify the size of the normalized power iterations.

Definition at line 237 of file randomized_svd.hpp.

◆ MaxIterations() [1/2]

size_t MaxIterations ( ) const

inline

Get the number of iterations for the power method.

Definition at line 240 of file randomized_svd.hpp.

◆ MaxIterations() [2/2]

size_t& MaxIterations ( )

inline

Modify the number of iterations for the power method.

Definition at line 242 of file randomized_svd.hpp.

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

/home/ryan/src/mlpack.org/_src/mlpack-git/src/mlpack/methods/randomized_svd/randomized_svd.hpp

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ RandomizedSVD() [1/2]

◆ RandomizedSVD() [2/2]

Member Function Documentation

◆ Apply() [1/3]

◆ Apply() [2/3]

◆ Apply() [3/3]

◆ Epsilon() [1/2]

◆ Epsilon() [2/2]

◆ IteratedPower() [1/2]

◆ IteratedPower() [2/2]

◆ MaxIterations() [1/2]

◆ MaxIterations() [2/2]