mlpack::svd::RandomizedBlockKrylovSVD Class Reference

Randomized block krylov SVD is a matrix factorization that is based on randomized matrix approximation techniques, developed in in "Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decomposition". More...

#include <randomized_block_krylov_svd.hpp>

Public Member Functions
	RandomizedBlockKrylovSVD (const arma::mat &data, arma::mat &u, arma::vec &s, arma::mat &v, const size_t maxIterations=2, const size_t rank=0, const size_t blockSize=0)
	Create object for the randomized block krylov SVD method. More...
	RandomizedBlockKrylovSVD (const size_t maxIterations=2, const size_t blockSize=0)
	Create object for the randomized block krylov 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 block krylov SVD. More...
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.
size_t	BlockSize () const
	Get the block size.
size_t &	BlockSize ()
	Modify the block size.

Detailed Description

Randomized block krylov SVD is a matrix factorization that is based on randomized matrix approximation techniques, developed in in "Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decomposition".

For more information, see the following.

@inproceedings{Musco2015,
  author    = {Cameron Musco and Christopher Musco},
  title     = {Randomized Block Krylov Methods for Stronger and Faster
               Approximate Singular Value Decomposition},
  booktitle = {Advances in Neural Information Processing Systems 28: Annual
               Conference on Neural Information Processing Systems 2015,
               December 7-12, 2015, Montreal, Quebec, Canada},
  pages     = {1396--1404},
  year      = {2015},
}

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 RandomizedBlockKrylovSVD object.
RandomizedBlockKrylovSVD bSVD();

arma::mat u, s, v;

// Use the Apply() method to get a factorization.
bSVD.Apply(data, u, s, v, rank);

Constructor & Destructor Documentation

RandomizedBlockKrylovSVD() [1/2]

mlpack::svd::RandomizedBlockKrylovSVD::RandomizedBlockKrylovSVD	(	const arma::mat &	data,
		arma::mat &	u,
		arma::vec &	s,
		arma::mat &	v,
		const size_t	maxIterations = 2,
		const size_t	rank = 0,
		const size_t	blockSize = 0
	)

Create object for the randomized block krylov SVD method.

Parameters

data	Data matrix.
u	First unitary matrix.
v	Second unitary matrix.
s	Diagonal matrix of singular values.
maxIterations	Number of iterations for the power method (Default: 2).
rank	Rank of the approximation (Default: number of rows.)
blockSize	The block size, must be >= rank (Default: rank + 10).

RandomizedBlockKrylovSVD() [2/2]

mlpack::svd::RandomizedBlockKrylovSVD::RandomizedBlockKrylovSVD	(	const size_t	maxIterations = 2,
		const size_t	blockSize = 0
	)

Create object for the randomized block krylov SVD method.

Parameters

maxIterations	Number of iterations for the power method (Default: 2).
blockSize	The block size, must be >= rank (Default: rank + 10).

Member Function Documentation

Apply()

void mlpack::svd::RandomizedBlockKrylovSVD::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 block krylov SVD.

Parameters

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

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

• src/mlpack/methods/block_krylov_svd/randomized_block_krylov_svd.hpp
• src/mlpack/methods/block_krylov_svd/randomized_block_krylov_svd.cpp