MatrixCompletion Class Reference

This class implements the popular nuclear norm minimization heuristic for matrix completion problems. More...

Public Member Functions
	MatrixCompletion (const size_t m, const size_t n, const arma::umat &indices, const arma::vec &values, const size_t r)
	Construct a matrix completion problem, specifying the maximum rank of the solution. More...
	MatrixCompletion (const size_t m, const size_t n, const arma::umat &indices, const arma::vec &values, const arma::mat &initialPoint)
	Construct a matrix completion problem, specifying the initial point of the optimization. More...
	MatrixCompletion (const size_t m, const size_t n, const arma::umat &indices, const arma::vec &values)
	Construct a matrix completion problem. More...
void	Recover (arma::mat &recovered)
	Solve the underlying SDP to fill in the remaining values. More...
const ens::LRSDP< ens::SDP< arma::sp_mat > > &	Sdp () const
	Return the underlying SDP. More...
ens::LRSDP< ens::SDP< arma::sp_mat > > &	Sdp ()
	Modify the underlying SDP. More...

Detailed Description

This class implements the popular nuclear norm minimization heuristic for matrix completion problems.

That is, given known values M_ij's, the following optimization problem (semi-definite program) is solved to fill in the remaining unknown values of X

min ||X||_* subj to X_ij = M_ij

where ||X||_* denotes the nuclear norm (sum of singular values of X).

For a theoretical treatment of the conditions necessary for exact recovery, see the following paper:

A Simpler Appoarch to Matrix Completion. Benjamin Recht. JMLR 11. http://arxiv.org/pdf/0910.0651v2.pdf

An example of how to use this class is shown below:

size_t m, n;         // size of unknown matrix
arma::umat indices;  // contains the known indices [2 x n_entries]
arma::vec values;    // contains the known values [n_entries]
arma::mat recovered; // will contain the completed matrix

MatrixCompletion mc(m, n, indices, values);
mc.Recover(recovered);

See also

LRSDP

Definition at line 53 of file matrix_completion.hpp.

Constructor & Destructor Documentation

MatrixCompletion() [1/3]

MatrixCompletion	(	const size_t	m,
		const size_t	n,
		const arma::umat &	indices,
		const arma::vec &	values,
		const size_t	r
	)

Construct a matrix completion problem, specifying the maximum rank of the solution.

Parameters

m	Number of rows of original matrix.
n	Number of columns of original matrix.
indices	Matrix containing the indices of the known entries (must be [2 x p]).
values	Vector containing the values of the known entries (must be length p).
r	Maximum rank of solution.

MatrixCompletion() [2/3]

MatrixCompletion	(	const size_t	m,
		const size_t	n,
		const arma::umat &	indices,
		const arma::vec &	values,
		const arma::mat &	initialPoint
	)

Construct a matrix completion problem, specifying the initial point of the optimization.

Parameters

m	Number of rows of original matrix.
n	Number of columns of original matrix.
indices	Matrix containing the indices of the known entries (must be [2 x p]).
values	Vector containing the values of the known entries (must be length p).
initialPoint	Starting point for the SDP optimization.

MatrixCompletion() [3/3]

MatrixCompletion	(	const size_t	m,
		const size_t	n,
		const arma::umat &	indices,
		const arma::vec &	values
	)

Construct a matrix completion problem.

Parameters

m	Number of rows of original matrix.
n	Number of columns of original matrix.
indices	Matrix containing the indices of the known entries (must be [2 x p]).
values	Vector containing the values of the known entries (must be length p).

Member Function Documentation

Recover()

void Recover

(

arma::mat &

recovered

)

Solve the underlying SDP to fill in the remaining values.

Parameters

recovered

Will contain the completed matrix.

Sdp() [1/2]

const ens::LRSDP<ens::SDP<arma::sp_mat> >& Sdp ( ) const

inline

Return the underlying SDP.

Definition at line 115 of file matrix_completion.hpp.

Sdp() [2/2]

ens::LRSDP<ens::SDP<arma::sp_mat> >& Sdp ( )

inline

Modify the underlying SDP.

Definition at line 120 of file matrix_completion.hpp.

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

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