The Gaussian mixture model Kmm_sk is an isotrope Gaussian mixture model on a kernel space. More...

#include <STK_Kmm_sk.h>

Inheritance diagram for STK::Kmm_sk:

Public Types
typedef KmmBase< Kmm_sk >	Base

Public Types inherited from STK::KmmBase< Kmm_sk >
typedef IMixtureDensity< Kmm_sk >	Base

typedef hidden::MixtureTraits< Kmm_sk >::Array	Array

Public Types inherited from STK::IMixtureDensity< Derived >
typedef hidden::MixtureTraits< Derived >::Array	Array

typedef hidden::MixtureTraits< Derived >::Parameters	Parameters

typedef hidden::Traits< Array >::Type	Type

Public Member Functions
	Kmm_sk (int nbCluster)
	default constructor

	Kmm_sk (Kmm_sk const &model)
	copy constructor

	~Kmm_sk ()
	destructor

int	computeNbFreeParameters () const

Real	lnComponentProbability (int i, int k) const

void	randomInit (CArrayXX const const &p_tik, CPointX const const &p_tk)
	Initialize randomly the variances of the Gaussian kernel mixture.

bool	run (CArrayXX const const &p_tik, CPointX const const &p_tk)
	update the variances.

Public Member Functions inherited from STK::KmmBase< Kmm_sk >
Real	sigma2 (int k) const

Real	dim (int k) const

Kernel::IKernel const *const	p_kernel () const

CArrayXX	dik () const

void	setDim (Real const &dim)
	set the dimensions of the kernel mixture model using an unique value

void	setDim (ExprBase< Vector > const &dim)
	set the dimension of the kernel mixture model

void	setKernel (Kernel::IKernel const *p_kernel)
	set the dimensions of the kernel mixture model using an unique value.

Real	impute (int i, int j, Weights const &pk) const

Real	rand (int i, int j, int k) const

void	getParameters (ArrayParam &params) const
	This function is used in order to get the current values of the parameters in an array.

void	writeParameters (CArrayXX const *p_tik, ostream &os) const
	This function can be used to write summary of parameters to the output stream.

int	nbSample () const

int	nbCluster () const

Public Member Functions inherited from STK::IMixtureDensity< Derived >
	~IMixtureDensity ()
	destructor

int	nbCluster () const

int	nbSample () const

Real	lnNbSample () const

Array const *const &	p_data () const

Parameters const &	param () const

void	setData (Array const &data)
	Set the data set.

void	setData (Array const &data, int nbRow, int nbCol, bool byRow=true)
	Set the data set and give dimensions.

bool	initializeStep ()
	This function will be called at the beginning of the estimation process once the model is created and data is set.

void	setParametersStep ()
	set the parameters obtained with the intermediate results and release the intermediate results.

void	finalizeStep ()
	This function will be called once the model is estimated.

template<class Weights >
Type	sample (int i, int j, Weights const &tk) const

Public Member Functions inherited from STK::IRecursiveTemplate< Derived >
Derived &	asDerived ()
	static cast : return a reference of this with a cast to the derived class.

Derived const &	asDerived () const
	static cast : return a const reference of this with a cast to the derived class.

Derived *	asPtrDerived ()
	static cast : return a ptr on a `Derived` of this with a cast to the derived class.

Derived const *	asPtrDerived () const
	static cast : return a ptr on a constant `Derived` of this with a cast to the derived class.

Derived *	clone () const
	create a leaf using the copy constructor of the Derived class.

Derived *	clone (bool isRef) const
	create a leaf using the copy constructor of the Derived class and a flag determining if the clone is a reference or not.

Additional Inherited Members
Public Attributes inherited from STK::KmmBase< Kmm_sk >
Parameters	param_
	parameters of the derived mixture model.

Protected Member Functions inherited from STK::KmmBase< Kmm_sk >
	KmmBase (int nbCluster)
	default constructor

	KmmBase (KmmBase const &model)
	copy constructor

	~KmmBase ()
	destructor

void	initializeModel ()
	Initialize the model before its first use.

void	compute_dik (CArrayXX const p_tik, CPointX const p_tk)
	compute the distance of the ith individual to the kth centroid

void	initializeModelImpl ()
	default implementation of initializeModelImpl (do nothing)

Protected Member Functions inherited from STK::IMixtureDensity< Derived >
	IMixtureDensity (int nbCluster)
	Default constructor.

	IMixtureDensity (IMixtureDensity const &model)
	copy constructor.

void	initializeModel ()
	Initialize the model before its first use.

bool	initializeStepImpl ()
	default implementation of initializeStepImpl (do nothing and return true)

void	finalizeStepImpl ()
	default implementation of finalizeStepImpl (do nothing)

void	setNbSample (int nbSample)
	Set the number of sample of the model (needed by kernel models)

Protected Member Functions inherited from STK::IRecursiveTemplate< Derived >
	IRecursiveTemplate ()
	constructor.

	~IRecursiveTemplate ()
	destructor.

Protected Attributes inherited from STK::KmmBase< Kmm_sk >
Kernel::IKernel const *	p_kernel_
	pointer on the kernel

CArrayXX	dik_
	Array of the intermediate results dik.

Protected Attributes inherited from STK::IMixtureDensity< Derived >
Parameters	param_
	parameters of the derived mixture model.

Detailed Description

The Gaussian mixture model Kmm_sk is an isotrope Gaussian mixture model on a kernel space.

It has a density function of the form

$f(\mathbf{x}|\theta) = \sum_{k=1}^K p_k \sum_{k=1}^K p_k \left(\frac{1}{\sqrt{2\pi}\sigma_k}\right)^{d_k} \exp\left\{ -\frac{\|\phi(x)-m_k\|^2}{2\sigma_k^2} \right\}$

where $\phi$ denote a feature mapping from the original space to an RKHS.

In a Kmm_sk model, the data set refer to the Gram's matrix.

Definition at line 75 of file STK_Kmm_sk.h.

Member Typedef Documentation

◆ Base

typedef KmmBase<Kmm_sk> STK::Kmm_sk::Base

Definition at line 78 of file STK_Kmm_sk.h.

Constructor & Destructor Documentation

◆ Kmm_sk() [1/2]

STK::Kmm_sk::Kmm_sk ( int nbCluster )

default constructor

Parameters

nbCluster number of cluster in the model

Definition at line 50 of file STK_Kmm_sk.cpp.

50: Base(nbCluster) {}

STK::KmmBase< Kmm_sk >::nbCluster

int nbCluster() const

Definition STK_IMixtureDensity.h:124

STK::Kmm_sk::Base

KmmBase< Kmm_sk > Base

Definition STK_Kmm_sk.h:78

◆ Kmm_sk() [2/2]

STK::Kmm_sk::Kmm_sk ( Kmm_sk const & model )

copy constructor

Parameters

model The model to copy

Definition at line 54 of file STK_Kmm_sk.cpp.

54: Base(model) {}

◆ ~Kmm_sk()

STK::Kmm_sk::~Kmm_sk ( )

destructor

Definition at line 56 of file STK_Kmm_sk.cpp.

56{}

Member Function Documentation

◆ computeNbFreeParameters()

int STK::Kmm_sk::computeNbFreeParameters ( ) const

Returns: the number of free parameters of the model

Definition at line 58 of file STK_Kmm_sk.cpp.

59{ return param_.dim_.sum() + this->nbCluster();}

STK::KmmBase< Kmm_sk >::param_

Parameters param_

parameters of the derived mixture model.

Definition STK_IMixtureDensity.h:180

References STK::KmmBase< Kmm_sk >::nbCluster(), and STK::KmmBase< Kmm_sk >::param_.

◆ lnComponentProbability()

Real STK::Kmm_sk::lnComponentProbability	(	int	i,
		int	k
	)		const

Returns: the value of the probability of the i-th sample in the k-th component.

Parameters

i,k	indexes of the sample and of the component

Definition at line 64 of file STK_Kmm_sk.cpp.

{
  return(- dik_.elt(i,k)/(2.*param_.sigma2_[k])
         - (std::log(param_.sigma2_[k]) +2.*Const::_LNSQRT2PI_)*param_.dim_[k]/2.);
}

References STK::KmmBase< Kmm_sk >::dik_, and STK::KmmBase< Kmm_sk >::param_.

◆ randomInit()

void STK::Kmm_sk::randomInit	(	CArrayXX const *const &	p_tik,
		CPointX const *const &	p_tk
	)

Initialize randomly the variances of the Gaussian kernel mixture.

Definition at line 71 of file STK_Kmm_sk.cpp.

{
#if STK_Kernel_DEBUG | STK_MIXTURE_VERBOSE
  stk_cout << _T("Entering Kmm_sk::randomInit( CArrayXX const* const& p_tik, CPointX const* const& p_tk)\n");
#endif
  compute_dik(p_tik, p_tk);
  param_.sigma2_ = sum( dik_.prod(*p_tik) )/ (*p_tk * param_.dim_)
                 + CPointX(p_tik->cols()).rand(Law::Normal(0, 0.05)).abs();
#ifdef STK_MIXTURE_VERY_VERBOSE
  stk_cout << _T("Kmm_sk::randomInit( CArrayXX const* const& p_tik, CPointX const* const& p_tk) done\n");
  stk_cout << param_.sigma2_ << "\n";
#endif
}

References _T, STK::KmmBase< Kmm_sk >::compute_dik(), STK::KmmBase< Kmm_sk >::dik_, STK::KmmBase< Kmm_sk >::param_, STK::ExprBase< Derived >::prod(), STK::KmmBase< Kmm_sk >::rand(), stk_cout, and STK::sum().

◆ run()

bool STK::Kmm_sk::run	(	CArrayXX const *const &	p_tik,
		CPointX const *const &	p_tk
	)

update the variances.

Definition at line 86 of file STK_Kmm_sk.cpp.

{
#if STK_Kernel_DEBUG | STK_MIXTURE_VERBOSE
  stk_cout << _T("Entering Kmm_sk::run( CArrayXX const* const& p_tik, CPointX const* const& p_tk)\n");
#endif
  compute_dik(p_tik, p_tk);
#ifdef STK_Kernel_DEBUG
  stk_cout<< _T("Stat::sumByCol( dik_.prod(*p_tik) ) =\n")  << Stat::sumByCol( dik_.prod(*p_tik) ) << "\n";
#endif
  param_.sigma2_ =  Stat::sumByCol( p_tik->prod(dik_) ) / (p_tk->prod(param_.dim_));
#ifdef STK_MIXTURE_VERBOSE
  stk_cout << _T("Kmm_sk::run( CArrayXX const* const& p_tik, CPointX const* const& p_tk) done\n");
  stk_cout << _T("sigma2 = ") << param_.sigma2_ << "\n";
#endif
  return true;
}

References _T, STK::KmmBase< Kmm_sk >::compute_dik(), STK::KmmBase< Kmm_sk >::dik_, STK::KmmBase< Kmm_sk >::param_, STK::ExprBase< Derived >::prod(), stk_cout, and STK::Stat::sumByCol().

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

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Base

Constructor & Destructor Documentation

◆ Kmm_sk() [1/2]

◆ Kmm_sk() [2/2]

◆ ~Kmm_sk()

Member Function Documentation

◆ computeNbFreeParameters()

◆ lnComponentProbability()

◆ randomInit()

◆ run()