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 52 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
mNumber of rows of original matrix.
nNumber of columns of original matrix.
indicesMatrix containing the indices of the known entries (must be [2 x p]).
valuesVector containing the values of the known entries (must be length p).
rMaximum 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
mNumber of rows of original matrix.
nNumber of columns of original matrix.
indicesMatrix containing the indices of the known entries (must be [2 x p]).
valuesVector containing the values of the known entries (must be length p).
initialPointStarting 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
mNumber of rows of original matrix.
nNumber of columns of original matrix.
indicesMatrix containing the indices of the known entries (must be [2 x p]).
valuesVector 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
recoveredWill 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 114 of file matrix_completion.hpp.

◆ Sdp() [2/2]

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

Modify the underlying SDP.

Definition at line 119 of file matrix_completion.hpp.


The documentation for this class was generated from the following file:
  • /home/jenkins-mlpack/mlpack.org/_src/mlpack-3.2.1/src/mlpack/methods/matrix_completion/matrix_completion.hpp