mlpack::svd::RandomizedSVD Class Reference

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...

#include <randomized_svd.hpp>

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...
size_t	IteratedPower () const
	Get the size of the normalized power iterations.
size_t &	IteratedPower ()
	Modify the size of the normalized power iterations.
size_t	MaxIterations () const
	Get the number of iterations for the power method.
size_t &	MaxIterations ()
	Modify the number of iterations for the power method.
double	Epsilon () const
	Get the value used for decomposition stability.
double &	Epsilon ()
	Modify the value used for decomposition stability.

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);

Constructor & Destructor Documentation

RandomizedSVD() [1/2]

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.
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]

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

Apply() [1/3]

void mlpack::svd::RandomizedSVD::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.

Apply() [2/3]

void mlpack::svd::RandomizedSVD::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]

template<typename MatType >

void mlpack::svd::RandomizedSVD::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.

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

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