#include <itkAdaptiveStochasticPreconditionedGradientDescentOptimizer.h>

Detailed Description

This class implements a gradient descent optimizer with adaptive gain.

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

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

The gain $a(t_k)$ at each iteration $k$ is defined by:

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

.

And the time $t_k$ is updated according to:

$t_{k+1} = [ t_k + sigmoid( -g_k^T P g_{k-1} ) ]^+$

where $g_k$ equals $dC/dx$ at iteration $k$ . For $t_0$ the InitialTime is used, which is defined in the the superclass (StandardGradientDescentOptimizer). Whereas in the superclass this parameter is superfluous, in this class it makes sense.

This method is described in the following references:

[1] Y. Qiao, B.P.F. Lelieveldt, M. Staring An efficient preconditioner for stochastic gradient descent optimization of image registration IEEE Transactions on Medical Imaging, 2019 https://doi.org/10.1109/TMI.2019.2897943

[2] P. Cruz Almost sure convergence and asymptotical normality of a generalization of Kesten's stochastic approximation algorithm for multidimensional case Technical Report, 2005. http://hdl.handle.net/2052/74

[3] S. Klein, J.P.W. Pluim, M. Staring, M.A. Viergever Adaptive stochastic gradient descent optimisation for image registration International Journal of Computer Vision, vol. 81, no. 3, pp. 227-239, 2009 http://dx.doi.org/10.1007/s11263-008-0168-y

It is very suitable to be used in combination with a stochastic estimate of the gradient $dC/dx$ . For example, in image registration problems it is often advantageous to compute the metric derivative ( $dC/dx$ ) 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:

See also: StochasticPreconditionedGradientDescent, AdaptiveStochasticGradientDescentOptimizer

Definition at line 78 of file itkAdaptiveStochasticPreconditionedGradientDescentOptimizer.h.

Inheritance diagram for itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer:

[legend]

Public Types
using	ConstPointer = SmartPointer< const Self >

using	Pointer = SmartPointer< Self >

using	Self = AdaptiveStochasticPreconditionedGradientDescentOptimizer

using	Superclass = StochasticPreconditionedGradientDescentOptimizer

Public Types inherited from itk::StochasticPreconditionedGradientDescentOptimizer
using	ConstPointer = SmartPointer< const Self >

using	Pointer = SmartPointer< Self >

using	PreconditionType = vnl_sparse_matrix< PreconditionValueType >

using	PreconditionValueType = DerivativeType::ValueType

using	ScaledCostFunctionPointer = ScaledCostFunctionType::Pointer

using	ScaledCostFunctionType = ScaledSingleValuedCostFunction

using	ScalesType = NonLinearOptimizer::ScalesType

using	Self = StochasticPreconditionedGradientDescentOptimizer

enum	StopConditionType

using	Superclass = PreconditionedGradientDescentOptimizer

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

using	Pointer = SmartPointer< Self >

using	PreconditionType = vnl_sparse_matrix< PreconditionValueType >

using	PreconditionValueType = DerivativeType::ValueType

using	ScaledCostFunctionPointer = ScaledCostFunctionType::Pointer

using	ScaledCostFunctionType = ScaledSingleValuedCostFunction

using	ScalesType = NonLinearOptimizer::ScalesType

using	Self = PreconditionedGradientDescentOptimizer

enum	StopConditionType { MaximumNumberOfIterations , MetricError , MinimumStepSize }

using	Superclass = ScaledSingleValuedNonLinearOptimizer

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

using	Pointer = SmartPointer< Self >

using	ScaledCostFunctionPointer = ScaledCostFunctionType::Pointer

using	ScaledCostFunctionType = ScaledSingleValuedCostFunction

using	ScalesType = NonLinearOptimizer::ScalesType

using	Self = ScaledSingleValuedNonLinearOptimizer

using	Superclass = SingleValuedNonLinearOptimizer

Public Member Functions
virtual const char *	GetClassName () const

virtual double	GetSigmoidMax () const

virtual double	GetSigmoidMin () const

virtual double	GetSigmoidScale () const

virtual bool	GetUseAdaptiveStepSizes () const

	ITK_DISALLOW_COPY_AND_MOVE (AdaptiveStochasticPreconditionedGradientDescentOptimizer)

virtual void	SetSigmoidMax (double _arg)

virtual void	SetSigmoidMin (double _arg)

virtual void	SetSigmoidScale (double _arg)

virtual void	SetUseAdaptiveStepSizes (bool _arg)

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

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

	ITK_DISALLOW_COPY_AND_MOVE (StochasticPreconditionedGradientDescentOptimizer)

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 ()

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

const cholmod_common *	GetCholmodCommon () const

const cholmod_factor *	GetCholmodFactor () 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 ()

	ITK_DISALLOW_COPY_AND_MOVE (PreconditionedGradientDescentOptimizer)

virtual void	MetricErrorResponse (ExceptionObject &err)

virtual void	ResumeOptimization ()

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 ()

virtual void	StopOptimization ()

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

const ParametersType &	GetCurrentPosition () const override

virtual bool	GetMaximize () const

virtual const ScaledCostFunctionType *	GetScaledCostFunction ()

virtual const ParametersType &	GetScaledCurrentPosition ()

bool	GetUseScales () const

virtual void	InitializeScales ()

	ITK_DISALLOW_COPY_AND_MOVE (ScaledSingleValuedNonLinearOptimizer)

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::StochasticPreconditionedGradientDescentOptimizer
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
	AdaptiveStochasticPreconditionedGradientDescentOptimizer ()

virtual void	UpdateCurrentTime ()

virtual	~AdaptiveStochasticPreconditionedGradientDescentOptimizer ()

Protected Member Functions inherited from itk::StochasticPreconditionedGradientDescentOptimizer
virtual double	Compute_a (double k) const

	StochasticPreconditionedGradientDescentOptimizer ()

virtual void	UpdateCurrentTime ()

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=default

Protected Attributes
DerivativeType	m_PreviousSearchDirection

Protected Attributes inherited from itk::StochasticPreconditionedGradientDescentOptimizer
double	m_CurrentTime { 0.0 }

Protected Attributes inherited from itk::PreconditionedGradientDescentOptimizer
cholmod_common *	m_CholmodCommon

cholmod_factor *	m_CholmodFactor { nullptr }

cholmod_sparse *	m_CholmodGradient { nullptr }

double	m_ConditionNumber { 1.0 }

DerivativeType	m_Gradient

double	m_LargestEigenValue { 1.0 }

double	m_LearningRate { 1.0 }

DerivativeType	m_SearchDirection

double	m_Sparsity { 1.0 }

StopConditionType	m_StopCondition { MaximumNumberOfIterations }

Protected Attributes inherited from itk::ScaledSingleValuedNonLinearOptimizer
ScaledCostFunctionPointer	m_ScaledCostFunction

ParametersType	m_ScaledCurrentPosition

Private Attributes
double	m_SigmoidMax { 1.0 }

double	m_SigmoidMin { -0.8 }

double	m_SigmoidScale { 1e-8 }

bool	m_UseAdaptiveStepSizes { true }

Additional Inherited Members
Protected Types inherited from itk::PreconditionedGradientDescentOptimizer
using	cholmod_l = int CInt

Member Typedef Documentation

◆ ConstPointer

using itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::ConstPointer = SmartPointer<const Self>

Definition at line 88 of file itkAdaptiveStochasticPreconditionedGradientDescentOptimizer.h.

◆ Pointer

using itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::Pointer = SmartPointer<Self>

Definition at line 87 of file itkAdaptiveStochasticPreconditionedGradientDescentOptimizer.h.

◆ Self

using itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::Self = AdaptiveStochasticPreconditionedGradientDescentOptimizer

Standard ITK.

Definition at line 84 of file itkAdaptiveStochasticPreconditionedGradientDescentOptimizer.h.

◆ Superclass

using itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::Superclass = StochasticPreconditionedGradientDescentOptimizer

Definition at line 85 of file itkAdaptiveStochasticPreconditionedGradientDescentOptimizer.h.

Constructor & Destructor Documentation

◆ AdaptiveStochasticPreconditionedGradientDescentOptimizer()

itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::AdaptiveStochasticPreconditionedGradientDescentOptimizer ( )

protected

◆ ~AdaptiveStochasticPreconditionedGradientDescentOptimizer()

virtual itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::~AdaptiveStochasticPreconditionedGradientDescentOptimizer ( )

inlineprotectedvirtual

Definition at line 133 of file itkAdaptiveStochasticPreconditionedGradientDescentOptimizer.h.

Member Function Documentation

◆ GetClassName()

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

virtual

Run-time type information (and related methods).

Reimplemented from itk::StochasticPreconditionedGradientDescentOptimizer.

Reimplemented in elastix::PreconditionedGradientDescent< TElastix >.

◆ GetSigmoidMax()

virtual double itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::GetSigmoidMax ( ) const

virtual

◆ GetSigmoidMin()

virtual double itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::GetSigmoidMin ( ) const

virtual

◆ GetSigmoidScale()

virtual double itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::GetSigmoidScale ( ) const

virtual

◆ GetUseAdaptiveStepSizes()

virtual bool itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::GetUseAdaptiveStepSizes ( ) const

virtual

◆ ITK_DISALLOW_COPY_AND_MOVE()

itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::ITK_DISALLOW_COPY_AND_MOVE ( AdaptiveStochasticPreconditionedGradientDescentOptimizer )

◆ New()

static Pointer itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::New ( )

static

Method for creation through the object factory.

◆ SetSigmoidMax()

virtual void itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::SetSigmoidMax ( double _arg )

virtual

Set/Get the maximum of the sigmoid. Should be >0. Default: 1.0

◆ SetSigmoidMin()

virtual void itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::SetSigmoidMin ( double _arg )

virtual

Set/Get the maximum of the sigmoid. Should be <0. Default: -0.8

◆ SetSigmoidScale()

virtual void itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::SetSigmoidScale ( double _arg )

virtual

Set/Get the scaling of the sigmoid width. Large values cause a more wide sigmoid. Default: 1e-8. Should be >0.

◆ SetUseAdaptiveStepSizes()

virtual void itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::SetUseAdaptiveStepSizes ( bool _arg )

virtual

Set/Get whether the adaptive step size mechanism is desired. Default: true

◆ UpdateCurrentTime()

virtual void itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::UpdateCurrentTime ( )

protectedvirtual

Function to update the current time If UseAdaptiveStepSizes is false this function just increments the CurrentTime by $E_0 = (sigmoid_{max} + sigmoid_{min})/2$ . Else, the CurrentTime is updated according to:
time = max[ 0, time + sigmoid( -gradient*previoussearchdirection) ]
In that case, also the m_PreviousSearchDirection is updated.

Reimplemented from itk::StochasticPreconditionedGradientDescentOptimizer.

Field Documentation

◆ m_PreviousSearchDirection

DerivativeType itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::m_PreviousSearchDirection

protected

The Previous search direction = P g, necessary for the CruzAcceleration

Definition at line 146 of file itkAdaptiveStochasticPreconditionedGradientDescentOptimizer.h.

◆ m_SigmoidMax

double itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::m_SigmoidMax { 1.0 }

private

Definition at line 151 of file itkAdaptiveStochasticPreconditionedGradientDescentOptimizer.h.

◆ m_SigmoidMin

double itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::m_SigmoidMin { -0.8 }

private

Definition at line 152 of file itkAdaptiveStochasticPreconditionedGradientDescentOptimizer.h.

◆ m_SigmoidScale

double itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::m_SigmoidScale { 1e-8 }

private

Definition at line 153 of file itkAdaptiveStochasticPreconditionedGradientDescentOptimizer.h.

◆ m_UseAdaptiveStepSizes

bool itk::AdaptiveStochasticPreconditionedGradientDescentOptimizer::m_UseAdaptiveStepSizes { true }

private

Settings

Definition at line 150 of file itkAdaptiveStochasticPreconditionedGradientDescentOptimizer.h.

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Private Attributes

Additional Inherited Members

Member Typedef Documentation

◆ ConstPointer

◆ Pointer

◆ Self

◆ Superclass

Constructor & Destructor Documentation

◆ AdaptiveStochasticPreconditionedGradientDescentOptimizer()

◆ ~AdaptiveStochasticPreconditionedGradientDescentOptimizer()

Member Function Documentation

◆ GetClassName()

◆ GetSigmoidMax()

◆ GetSigmoidMin()

◆ GetSigmoidScale()

◆ GetUseAdaptiveStepSizes()

◆ ITK_DISALLOW_COPY_AND_MOVE()

◆ New()

◆ SetSigmoidMax()

◆ SetSigmoidMin()

◆ SetSigmoidScale()

◆ SetUseAdaptiveStepSizes()

◆ UpdateCurrentTime()

Field Documentation

◆ m_PreviousSearchDirection

◆ m_SigmoidMax

◆ m_SigmoidMin

◆ m_SigmoidScale

◆ m_UseAdaptiveStepSizes