Atoms Class Reference

Class to hold the information and operations of current atoms in the soluton space. More...

Public Member Functions
	Atoms ()
void	AddAtom (const arma::vec &v, FuncSq &function, const double c=0)
	Add atom into the solution space. More...
const arma::mat &	CurrentAtoms () const
	Get the current atoms. More...
arma::mat &	CurrentAtoms ()
	Modify the current atoms. More...
const arma::vec &	CurrentCoeffs () const
	Get the current atom coefficients. More...
arma::vec &	CurrentCoeffs ()
	Modify the current atom coefficients. More...
void	ProjectedGradientEnhancement (FuncSq &function, double tau, double stepSize, size_t maxIteration=100, double tolerance=1e-3)
	Enhance the solution in the convex hull of current atoms with atom norm constraint tau. More...
void	PruneSupport (const double F, FuncSq &function)
	Prune the support, delete previous atoms if they don't contribute much. More...
void	RecoverVector (arma::mat &x)
	Recover the solution coordinate from the coefficients of current atoms. More...

Detailed Description

Class to hold the information and operations of current atoms in the soluton space.

Definition at line 25 of file atoms.hpp.

Constructor & Destructor Documentation

Atoms()

Atoms ( )

inline

Definition at line 28 of file atoms.hpp.

Member Function Documentation

AddAtom()

void AddAtom ( const arma::vec &  v, FuncSq &  function, const double  c = 0  )

inline

Add atom into the solution space.

Parameters

v	new atom to be added.
c	coefficient of the new atom.

Definition at line 36 of file atoms.hpp.

References Atoms::CurrentAtoms(), and Atoms::CurrentCoeffs().

Referenced by UpdateSpan::Update(), and UpdateFullCorrection::Update().

CurrentAtoms() [1/2]

const arma::mat& CurrentAtoms ( ) const

inline

Get the current atoms.

Definition at line 203 of file atoms.hpp.

Referenced by Atoms::AddAtom(), and UpdateSpan::Update().

CurrentAtoms() [2/2]

arma::mat& CurrentAtoms ( )

inline

Modify the current atoms.

Definition at line 205 of file atoms.hpp.

CurrentCoeffs() [1/2]

const arma::vec& CurrentCoeffs ( ) const

inline

Get the current atom coefficients.

Definition at line 198 of file atoms.hpp.

Referenced by Atoms::AddAtom(), UpdateSpan::Update(), and UpdateFullCorrection::Update().

CurrentCoeffs() [2/2]

arma::vec& CurrentCoeffs ( )

inline

Modify the current atom coefficients.

Definition at line 200 of file atoms.hpp.

ProjectedGradientEnhancement()

void ProjectedGradientEnhancement ( FuncSq &  function, double  tau, double  stepSize, size_t  maxIteration = 100, double  tolerance = 1e-3  )

inline

Enhance the solution in the convex hull of current atoms with atom norm constraint tau.

Used in UpdateFullCorrection class for update step.

Minimize the function in the atom domain defined by current atoms, where the solution still need to have atom norm (defined by current atoms) less than or equal to tau. We use projected gradient method to solve it, see the "Enhancement step" of the following paper:

@article{RaoShaWri:2015Forward--backward,
   Author = {Rao, Nikhil and Shah, Parikshit and Wright, Stephen},
   Journal = {IEEE Transactions on Signal Processing},
   Number = {21},
   Pages = {5798--5811},
   Publisher = {IEEE},
   Title = {Forward--backward greedy algorithms for atomic norm regularization},
   Volume = {63},
   Year = {2015}
}

Parameters

function	function to be minimized.
tau	atom norm constraint.
stepSize	step size for projected gradient method.
maxIteration	maximum iteration number.
tolerance	tolerance for projected gradient method.

Definition at line 165 of file atoms.hpp.

References Proximal::ProjectToL1Ball(), and Atoms::RecoverVector().

Referenced by UpdateFullCorrection::Update().

PruneSupport()

void PruneSupport ( const double  F, FuncSq &  function  )

inline

Prune the support, delete previous atoms if they don't contribute much.

See Algorithm 2 of paper:

@article{RaoShaWri:2015Forward--backward,
   Author = {Rao, Nikhil and Shah, Parikshit and Wright, Stephen},
   Journal = {IEEE Transactions on Signal Processing},
   Number = {21},
   Pages = {5798--5811},
   Publisher = {IEEE},
   Title = {Forward--backward greedy algorithms for atomic norm regularization},
   Volume = {63},
   Year = {2015}
}

Parameters

F	thresholding number.
function	function to be optimized.

Definition at line 85 of file atoms.hpp.

References Atoms::RecoverVector().

Referenced by UpdateSpan::Update().

RecoverVector()

void RecoverVector ( arma::mat &  x )

inline

Recover the solution coordinate from the coefficients of current atoms.

Definition at line 61 of file atoms.hpp.

Referenced by Atoms::ProjectedGradientEnhancement(), Atoms::PruneSupport(), UpdateSpan::Update(), and UpdateFullCorrection::Update().

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

• src/mlpack/core/optimizers/fw/atoms.hpp