#include <itkStochasticPreconditionedGradientDescentOptimizer.h>

Detailed Description

This class implements a gradient descent optimizer with a decaying gain and preconditioning.

If is a cost function that has to be minimized, the following iterative algorithm is used to find the optimal parameters :

$x(k+1) = x(k) - a(k) P dC/dx$

The gain at each iteration is defined by:

$a(k) = a / (A + k + 1)^alpha$

.

It is very suitable to be used in combination with a stochastic estimate of the gradient . For example, in image registration problems it is often advantageous to compute the metric derivative ( ) on a new set of randomly selected image samples in each iteration. You may set the parameter NewSamplesEveryIteration to "true" to achieve this effect. For more information on this strategy, you may have a look at:

[1] S. Klein, M. Staring, J.P.W. Pluim, "Evaluation of Optimization Methods for Nonrigid Medical Image Registration using Mutual Information and B-Splines" IEEE Transactions on Image Processing, vol. 16 (12), December 2007.

This class also serves as a base class for other preconditioned GradientDescent type algorithms, like the AdaptiveStochasticPreconditionedGradientDescentOptimizer.

See also: StochasticPreconditionedGradientDescent, AdaptiveStochasticPreconditionedGradientDescentOptimizer

Definition at line 56 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

Inheritance diagram for itk::StochasticPreconditionedGradientDescentOptimizer:

Public Types
typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::CostFunctionType	CostFunctionType

typedef Superclass::DerivativeType	DerivativeType

typedef Superclass::MeasureType	MeasureType

typedef Superclass::ParametersType	ParametersType

typedef SmartPointer< Self >	Pointer

typedef Superclass::PreconditionType	PreconditionType

typedef Superclass::PreconditionValueType	PreconditionValueType

typedef Superclass::ScaledCostFunctionPointer	ScaledCostFunctionPointer

typedef Superclass::ScaledCostFunctionType	ScaledCostFunctionType

typedef Superclass::ScalesType	ScalesType

typedef StochasticPreconditionedGradientDescentOptimizer	Self

typedef Superclass::StopConditionType	StopConditionType

typedef PreconditionedGradientDescentOptimizer	Superclass

Public Types inherited from itk::PreconditionedGradientDescentOptimizer
typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::CostFunctionType	CostFunctionType

typedef Superclass::DerivativeType	DerivativeType

typedef Superclass::MeasureType	MeasureType

typedef Superclass::ParametersType	ParametersType

typedef SmartPointer< Self >	Pointer

typedef vnl_sparse_matrix< PreconditionValueType >	PreconditionType

typedef DerivativeType::ValueType	PreconditionValueType

typedef Superclass::ScaledCostFunctionPointer	ScaledCostFunctionPointer

typedef Superclass::ScaledCostFunctionType	ScaledCostFunctionType

typedef Superclass::ScalesType	ScalesType

typedef PreconditionedGradientDescentOptimizer	Self

enum	StopConditionType { MaximumNumberOfIterations , MetricError , MinimumStepSize }

typedef ScaledSingleValuedNonLinearOptimizer	Superclass

Public Types inherited from itk::ScaledSingleValuedNonLinearOptimizer
typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::CostFunctionType	CostFunctionType

typedef Superclass::DerivativeType	DerivativeType

typedef Superclass::MeasureType	MeasureType

typedef Superclass::ParametersType	ParametersType

typedef SmartPointer< Self >	Pointer

typedef ScaledCostFunctionType::Pointer	ScaledCostFunctionPointer

typedef ScaledSingleValuedCostFunction	ScaledCostFunctionType

typedef NonLinearOptimizer::ScalesType	ScalesType

typedef ScaledSingleValuedNonLinearOptimizer	Self

typedef SingleValuedNonLinearOptimizer	Superclass

Public Member Functions
virtual void	AdvanceOneStep (void)

virtual const char *	GetClassName () const

virtual double	GetCurrentTime () const

virtual double	GetInitialTime () const

virtual double	GetParam_a () const

virtual double	GetParam_A () const

virtual double	GetParam_alpha () const

virtual void	SetInitialTime (double _arg)

virtual void	SetParam_a (double _arg)

virtual void	SetParam_A (double _arg)

virtual void	SetParam_alpha (double _arg)

virtual void	StartOptimization (void)

Public Member Functions inherited from itk::PreconditionedGradientDescentOptimizer
virtual void	AdvanceOneStep (void)

const cholmod_common *	GetCholmodCommon (void) const

const cholmod_factor *	GetCholmodFactor (void) const

virtual const char *	GetClassName () const

virtual double	GetConditionNumber () const

virtual unsigned int	GetCurrentIteration () const

virtual double	GetDiagonalWeight () const

virtual const DerivativeType &	GetGradient ()

virtual double	GetLargestEigenValue () const

virtual const double &	GetLearningRate ()

virtual double	GetMinimumGradientElementMagnitude () const

virtual const unsigned long &	GetNumberOfIterations ()

virtual const DerivativeType &	GetSearchDirection ()

virtual double	GetSparsity () const

virtual const StopConditionType &	GetStopCondition ()

virtual const double &	GetValue ()

virtual void	MetricErrorResponse (ExceptionObject &err)

virtual void	ResumeOptimization (void)

virtual void	SetDiagonalWeight (double _arg)

virtual void	SetLearningRate (double _arg)

virtual void	SetMinimumGradientElementMagnitude (double _arg)

virtual void	SetNumberOfIterations (unsigned long _arg)

virtual void	SetPreconditionMatrix (PreconditionType &precondition)

virtual void	StartOptimization (void)

virtual void	StopOptimization (void)

Public Member Functions inherited from itk::ScaledSingleValuedNonLinearOptimizer
virtual const char *	GetClassName () const

const ParametersType &	GetCurrentPosition (void) const override

virtual bool	GetMaximize () const

virtual const ScaledCostFunctionType *	GetScaledCostFunction ()

virtual const ParametersType &	GetScaledCurrentPosition ()

bool	GetUseScales (void) const

virtual void	InitializeScales (void)

virtual void	MaximizeOff ()

virtual void	MaximizeOn ()

void	SetCostFunction (CostFunctionType *costFunction) override

virtual void	SetMaximize (bool _arg)

virtual void	SetUseScales (bool arg)

Static Public Member Functions
static Pointer	New ()

Static Public Member Functions inherited from itk::PreconditionedGradientDescentOptimizer
static Pointer	New ()

Static Public Member Functions inherited from itk::ScaledSingleValuedNonLinearOptimizer
static Pointer	New ()

Protected Member Functions
virtual double	Compute_a (double k) const

	StochasticPreconditionedGradientDescentOptimizer ()

virtual void	UpdateCurrentTime (void)

virtual	~StochasticPreconditionedGradientDescentOptimizer ()

Protected Member Functions inherited from itk::PreconditionedGradientDescentOptimizer
virtual void	CholmodSolve (const DerivativeType &gradient, DerivativeType &searchDirection, int solveType=CHOLMOD_A)

	PreconditionedGradientDescentOptimizer ()

void	PrintSelf (std::ostream &os, Indent indent) const

virtual	~PreconditionedGradientDescentOptimizer ()

Protected Member Functions inherited from itk::ScaledSingleValuedNonLinearOptimizer
virtual void	GetScaledDerivative (const ParametersType &parameters, DerivativeType &derivative) const

virtual MeasureType	GetScaledValue (const ParametersType &parameters) const

virtual void	GetScaledValueAndDerivative (const ParametersType &parameters, MeasureType &value, DerivativeType &derivative) const

void	PrintSelf (std::ostream &os, Indent indent) const override

	ScaledSingleValuedNonLinearOptimizer ()

void	SetCurrentPosition (const ParametersType &param) override

virtual void	SetScaledCurrentPosition (const ParametersType &parameters)

	~ScaledSingleValuedNonLinearOptimizer () override

Protected Attributes
double	m_CurrentTime

Protected Attributes inherited from itk::PreconditionedGradientDescentOptimizer
cholmod_common *	m_CholmodCommon

cholmod_factor *	m_CholmodFactor

cholmod_sparse *	m_CholmodGradient

double	m_ConditionNumber

DerivativeType	m_Gradient

double	m_LargestEigenValue

double	m_LearningRate

DerivativeType	m_SearchDirection

double	m_Sparsity

StopConditionType	m_StopCondition

Protected Attributes inherited from itk::ScaledSingleValuedNonLinearOptimizer
ScaledCostFunctionPointer	m_ScaledCostFunction

ParametersType	m_ScaledCurrentPosition

Private Member Functions
void	operator= (const Self &)

	StochasticPreconditionedGradientDescentOptimizer (const Self &)

Private Attributes
double	m_InitialTime

double	m_Param_a

double	m_Param_A

double	m_Param_alpha

Additional Inherited Members
Protected Types inherited from itk::PreconditionedGradientDescentOptimizer
typedef int	CInt

Member Typedef Documentation

◆ ConstPointer

typedef SmartPointer<const Self> itk::StochasticPreconditionedGradientDescentOptimizer::ConstPointer

Definition at line 66 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ CostFunctionType

typedef Superclass::CostFunctionType itk::StochasticPreconditionedGradientDescentOptimizer::CostFunctionType

Definition at line 78 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ DerivativeType

typedef Superclass::DerivativeType itk::StochasticPreconditionedGradientDescentOptimizer::DerivativeType

Definition at line 77 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ MeasureType

typedef Superclass::MeasureType itk::StochasticPreconditionedGradientDescentOptimizer::MeasureType

Typedefs inherited from the superclass.

Definition at line 75 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ ParametersType

typedef Superclass::ParametersType itk::StochasticPreconditionedGradientDescentOptimizer::ParametersType

Definition at line 76 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ Pointer

typedef SmartPointer<Self> itk::StochasticPreconditionedGradientDescentOptimizer::Pointer

Definition at line 65 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ PreconditionType

typedef Superclass::PreconditionType itk::StochasticPreconditionedGradientDescentOptimizer::PreconditionType

Definition at line 86 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ PreconditionValueType

typedef Superclass::PreconditionValueType itk::StochasticPreconditionedGradientDescentOptimizer::PreconditionValueType

Some typedefs for computing the SelfHessian

Definition at line 85 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ ScaledCostFunctionPointer

typedef Superclass::ScaledCostFunctionPointer itk::StochasticPreconditionedGradientDescentOptimizer::ScaledCostFunctionPointer

Definition at line 81 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ ScaledCostFunctionType

typedef Superclass::ScaledCostFunctionType itk::StochasticPreconditionedGradientDescentOptimizer::ScaledCostFunctionType

Definition at line 80 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ ScalesType

typedef Superclass::ScalesType itk::StochasticPreconditionedGradientDescentOptimizer::ScalesType

Definition at line 79 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ Self

typedef StochasticPreconditionedGradientDescentOptimizer itk::StochasticPreconditionedGradientDescentOptimizer::Self

Standard ITK.

Definition at line 62 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ StopConditionType

typedef Superclass::StopConditionType itk::StochasticPreconditionedGradientDescentOptimizer::StopConditionType

Definition at line 82 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ Superclass

typedef PreconditionedGradientDescentOptimizer itk::StochasticPreconditionedGradientDescentOptimizer::Superclass

Definition at line 63 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

Constructor & Destructor Documentation

◆ StochasticPreconditionedGradientDescentOptimizer() [1/2]

itk::StochasticPreconditionedGradientDescentOptimizer::StochasticPreconditionedGradientDescentOptimizer ( )

protected

◆ ~StochasticPreconditionedGradientDescentOptimizer()

virtual itk::StochasticPreconditionedGradientDescentOptimizer::~StochasticPreconditionedGradientDescentOptimizer ( )

inlineprotectedvirtual

Definition at line 125 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ StochasticPreconditionedGradientDescentOptimizer() [2/2]

itk::StochasticPreconditionedGradientDescentOptimizer::StochasticPreconditionedGradientDescentOptimizer ( const Self & )

private

Member Function Documentation

◆ AdvanceOneStep()

virtual void itk::StochasticPreconditionedGradientDescentOptimizer::AdvanceOneStep ( void )

virtual

Sets a new LearningRate before calling the Superclass' implementation, and updates the current time.

Reimplemented from itk::PreconditionedGradientDescentOptimizer.

◆ Compute_a()

virtual double itk::StochasticPreconditionedGradientDescentOptimizer::Compute_a ( double k ) const

protectedvirtual

Function to compute the parameter at time/iteration k.

◆ GetClassName()

virtual const char * itk::StochasticPreconditionedGradientDescentOptimizer::GetClassName ( ) const

virtual

Run-time type information (and related methods).

Reimplemented from itk::PreconditionedGradientDescentOptimizer.

Reimplemented in elastix::PreconditionedGradientDescent< TElastix >, and itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer.

◆ GetCurrentTime()

virtual double itk::StochasticPreconditionedGradientDescentOptimizer::GetCurrentTime ( ) const

virtual

Get the current time. This equals the CurrentIteration in this base class but may be different in inheriting classes, such as the AccelerateGradientDescent.

◆ GetInitialTime()

virtual double itk::StochasticPreconditionedGradientDescentOptimizer::GetInitialTime ( ) const

virtual

◆ GetParam_a()

virtual double itk::StochasticPreconditionedGradientDescentOptimizer::GetParam_a ( ) const

virtual

◆ GetParam_A()

virtual double itk::StochasticPreconditionedGradientDescentOptimizer::GetParam_A ( ) const

virtual

◆ GetParam_alpha()

virtual double itk::StochasticPreconditionedGradientDescentOptimizer::GetParam_alpha ( ) const

virtual

◆ New()

static Pointer itk::StochasticPreconditionedGradientDescentOptimizer::New ( )

static

Method for creation through the object factory.

◆ operator=()

void itk::StochasticPreconditionedGradientDescentOptimizer::operator= ( const Self & )

private

◆ SetInitialTime()

virtual void itk::StochasticPreconditionedGradientDescentOptimizer::SetInitialTime ( double _arg )

virtual

Set/Get the initial time. Should be >=0. This function is superfluous, since Param_A does effectively the same. However, in inheriting classes, like the AcceleratedGradientDescent the initial time may have a different function than Param_A. Default: 0.0

◆ SetParam_a()

virtual void itk::StochasticPreconditionedGradientDescentOptimizer::SetParam_a ( double _arg )

virtual

Set/Get a.

◆ SetParam_A()

virtual void itk::StochasticPreconditionedGradientDescentOptimizer::SetParam_A ( double _arg )

virtual

Set/Get A.

◆ SetParam_alpha()

virtual void itk::StochasticPreconditionedGradientDescentOptimizer::SetParam_alpha ( double _arg )

virtual

Set/Get alpha.

◆ StartOptimization()

virtual void itk::StochasticPreconditionedGradientDescentOptimizer::StartOptimization ( void )

virtual

Set current time to 0 and call superclass' implementation.

Reimplemented from itk::PreconditionedGradientDescentOptimizer.

Reimplemented in elastix::PreconditionedGradientDescent< TElastix >.

◆ UpdateCurrentTime()

virtual void itk::StochasticPreconditionedGradientDescentOptimizer::UpdateCurrentTime ( void )

protectedvirtual

Function to update the current time This function just increments the CurrentTime by 1. Inheriting functions may implement something smarter, for example, dependent on the progress.

Reimplemented in itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer.

Field Documentation

◆ m_CurrentTime

double itk::StochasticPreconditionedGradientDescentOptimizer::m_CurrentTime

protected

The current time, which serves as input for Compute_a

Definition at line 138 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ m_InitialTime

double itk::StochasticPreconditionedGradientDescentOptimizer::m_InitialTime

private

Settings

Definition at line 151 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ m_Param_a

double itk::StochasticPreconditionedGradientDescentOptimizer::m_Param_a

private

Parameters, as described by Spall.

Definition at line 146 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ m_Param_A

double itk::StochasticPreconditionedGradientDescentOptimizer::m_Param_A

private

Definition at line 147 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

◆ m_Param_alpha

double itk::StochasticPreconditionedGradientDescentOptimizer::m_Param_alpha

private

Definition at line 148 of file itkStochasticPreconditionedGradientDescentOptimizer.h.

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Additional Inherited Members

Member Typedef Documentation

◆ ConstPointer

◆ CostFunctionType

◆ DerivativeType

◆ MeasureType

◆ ParametersType

◆ Pointer

◆ PreconditionType

◆ PreconditionValueType

◆ ScaledCostFunctionPointer

◆ ScaledCostFunctionType

◆ ScalesType

◆ Self

◆ StopConditionType

◆ Superclass

Constructor & Destructor Documentation

◆ StochasticPreconditionedGradientDescentOptimizer() [1/2]

◆ ~StochasticPreconditionedGradientDescentOptimizer()

◆ StochasticPreconditionedGradientDescentOptimizer() [2/2]

Member Function Documentation

◆ AdvanceOneStep()

◆ Compute_a()

◆ GetClassName()

◆ GetCurrentTime()

◆ GetInitialTime()

◆ GetParam_a()

◆ GetParam_A()

◆ GetParam_alpha()

◆ New()

◆ operator=()

◆ SetInitialTime()

◆ SetParam_a()

◆ SetParam_A()

◆ SetParam_alpha()

◆ StartOptimization()

◆ UpdateCurrentTime()

Field Documentation

◆ m_CurrentTime

◆ m_InitialTime

◆ m_Param_a

◆ m_Param_A

◆ m_Param_alpha