This class is a Gaussian Cluster wich is a specialization of MMSD_GaussianCluster. More...

#include <MMSD_ConstraintGaussianCluster.h>

Inheritance diagram for MMSD_ConstraintGaussianCluster:

Collaboration diagram for MMSD_ConstraintGaussianCluster:

Public Member Functions
virtual tString	toString () const
	turn the class into string More...

void	computeMultivariateDensity (double *Pk) const
	compute the probabities of samples to be in cluster This More...

void	computeMultivariateDensity (MMSD_DoubleVector &Pk) const
	compute the probabities of samples to be in cluster This More...

void	updateWeights (const MMSD_DoubleVector &probs)
	update the weights of the cluster More...

void	updateFreedomDegrees (const MMSD_DoubleVector &probs)
	update the freedom degrees More...

void	setWeightInitializationType (const tString &type, const double &shape, const double &rate)
	set the weight initialization type More...

void	setWeightInitializationType (const tFlag &t, const double &shape, const double &rate)
	set the weight initialization type More...

void	setWeightInitializationType (const tFlag &t)
	set the weight initialization type More...

void	setMaxFreedomDegreeValue (const double &v)
	set the max freedom degree value More...

double	getMaxFreedomDegreeValue () const
	get the max freedom degree value More...

double	getRate () const
	get rate of the cluster which is the percent of samples in this cluster. More...

const MMSD_DoubleFullMatrix &	getWeights () const
	get the weight of sample 's property of size NxP More...

const MMSD_DoubleVector &	getFreedomDegrees () const
	get the freedom degree of property of size P More...

void	setLaw (SP::MMSD_Law law)
	set the law More...

const MMSD_Law *	getLaw () const
	get the law More...

tBoolean	isEmpty () const
	return true is the cluster is empty More...

virtual void	restore (const MMSD_DoubleFullMatrix &properties)
	restore the unstored values after a backup More...

virtual void	initialize (const int &clusterIndex, const MMSD_IntegerVector &clusterIndexSamples, const MMSD_DoubleFullMatrix &properties)
	initialize the cluster More...

void	updateRate (const MMSD_DoubleVector &clusterProbabilitiesSamples)
	update the rate of the cluster More...

void	updateLaw (const MMSD_DoubleFullMatrix &properties, const MMSD_DoubleVector &probs)
	update the law parameters More...

void	sort ()
	sort the freedom degrees with respect to the law More...

void	setHasBeenLoaded (const tBoolean &v)
	set the if the object has completely been loaded More...

tBoolean	hasBeenLoaded () const
	return true if the object has completely been loaded More...

void	getSharedPointer (SP::CORE_Object &p)
	get the shared pointer of this class into p More...

void	getSharedPointer (SPC::CORE_Object &p) const
	get the shared pointer of this class into p More...

tString	getClassName () const
	return the class name of the object More...

tString	getIdentityString () const
	return the identity string of the object of the form className_at_address More...

tString	getPointerAddress () const
	return the identity string of the object More...

template<class T >
tBoolean	isInstanceOf () const
	return true if the object is an instance of T More...

virtual void	print ()
	print the class More...

virtual ostream &	print (ostream &out) const
	print the class More...

virtual void	print (const tString &message)
	print the class More...

virtual void	print (const tInteger &str)
	print More...

virtual void	print (const tRelativeInteger &str)
	print More...

virtual void	print (const tReal &str)
	print More...

virtual void	print (const int &str)
	print More...

Static Public Member Functions
static SP::MMSD_ConstraintGaussianCluster	New ()
	create an instance of gaussian law More...

static void	initSeed (const long int &v)
	init the seed with v value More...

static void	initSeed ()
	init the seed More...

static tString	getClassName (const tString &identityString)
	return the class name of the object using only the identity string More...

template<class T >
static tString	getTypeName ()
	get type name More...

static tBoolean	is64Architecture ()
	return true if the machine is a 64 bits machine More...

static tBoolean	is32Architecture ()
	return true if the machine is a 32 bits machine More...

static tString	pointer2String (const void *obj)
	return the string represantation of a pointer More...

static void	setOutput (ostream &out)
	set output More...

static ostream &	getOutput ()
	get output More...

static void	printObjectsInMemory ()
	print object in memory More...

static ostream &	print (ostream &out, const tString &message)
	print the class More...

static void	outputPrint (const tString &message)

Static Public Attributes
static tBoolean	mIsMemoryTesting =false
	indicator to store all classes created and deleted only for debuging version More...

Protected Member Functions
	MMSD_ConstraintGaussianCluster (void)
	create an object More...

virtual	~MMSD_ConstraintGaussianCluster (void)
	destroy an object. More...

virtual void	updateFreedomDegrees (const MMSD_DoubleFullMatrix &W, const MMSD_DoubleVector &probs, const double &maxFD, MMSD_DoubleVector &nus)
	update the freedom degrees from weights & probabilities. More...

MATH_Equation &	getSolver ()
	get the solver More...

MMSD_GaussianFDFunction &	getFunction ()
	get the function to find zero More...

virtual void	computeMultivariateDensity (const MMSD_DoubleFullMatrix &YP, const MMSD_DoubleFullMatrix &P, const MMSD_DoubleVector &D, const MMSD_DoubleVector &mean, const MMSD_DoubleVector &nu, double *Pk) const
	compute the probabities of samples to be in cluster This from law, freedom degrees & weights More...

virtual void	updateWeights (const MMSD_DoubleFullMatrix &YP, const MMSD_DoubleFullMatrix &P, const MMSD_DoubleVector &Diag, const MMSD_DoubleVector &mean, const MMSD_DoubleVector &nus, const MMSD_DoubleVector &probs, MMSD_DoubleFullMatrix &W) const
	compute the weights from law, freedom degrees & probabilites More...

virtual void	saveToUIClass (UI_Class &mclass) const
	how to save the object from a mate model class More...

virtual void	loadFromUIClass (const UI_Class &mclass)
	how to load the object from a Meta Model class More...

void	setThis (SP::CORE_Object p)
	set this weak shared pointer called toDoAfterThis setting method More...

virtual void	setType (tString type)
	set the type of the object More...

virtual void	toDoAfterThisSetting ()
	method called after setThis() method this method can oly be called once. More...

Detailed Description

This class is a Gaussian Cluster wich is a specialization of MMSD_GaussianCluster.

It defines the updating of freedomDegree: see MMSD_ConstraintGaussianCluster::updateFreedomDegrees()

Author: Stéphane Despréaux

Version: 1.0

Constructor & Destructor Documentation

MMSD_ConstraintGaussianCluster::MMSD_ConstraintGaussianCluster ( void )

protected

create an object

References CORE_Object::setType().

Referenced by New().

Here is the call graph for this function:

Here is the caller graph for this function:

MMSD_ConstraintGaussianCluster::~MMSD_ConstraintGaussianCluster ( void )

protectedvirtual

destroy an object.

Member Function Documentation

void MMSD_GaussianCluster::computeMultivariateDensity	(	const MMSD_DoubleFullMatrix &	YP,
		const MMSD_DoubleFullMatrix &	P,
		const MMSD_DoubleVector &	D,
		const MMSD_DoubleVector &	mean,
		const MMSD_DoubleVector &	nu,
		double *	Pk
	)		const

protectedvirtualinherited

compute the probabities of samples to be in cluster This from law, freedom degrees & weights

Parameters

YP	: Y.P matrix of size NxP
P	: P eigen value decomposition matrix of cov(Y) of size PXP
D	: D eigen value decomposition diagonal matrix of cov(Y) of size P
mean	: mean value of the properties cluster of size P
nu	: freedom degrees of the cluster of size P
Pk	: output vector which is the probability of the sample i to be in the cluster This. Must be of size N Pk=0 for j in [0,P[ d=D[j] s=<P[][j],mMean> nu=nu[j] t=(nu+1)/2 for i in [0,N[ R=(YP[i][j]-s)^2 / d Pk[i]+=LogGamma(t)-logGamma(nu/2)-(1/2).log(nu.PI)-(1/2).log(d)-t.log(1+(R/nu))

Implements MMSD_Cluster.

References MATH_LogGammaFunction::ComputeFunction(), LAP_DoubleFullGeneralMatrix::getColumnByReference(), LAP_DoubleFullGeneralMatrix::getColumnsNumber(), LAP_DoubleFullGeneralMatrix::getRowsNumber(), LAP_ConstVector< T >::getValues(), and LAP_ConstDoubleVector::product().

Here is the call graph for this function:

void MMSD_Cluster::computeMultivariateDensity ( double * Pk ) const

inlineinherited

compute the probabities of samples to be in cluster This

Referenced by MMSD_Cluster::computeMultivariateDensity(), and MMSD_Model::computeSampleClusterProbabilities().

Here is the caller graph for this function:

void MMSD_Cluster::computeMultivariateDensity ( MMSD_DoubleVector & Pk ) const

inlineinherited

compute the probabities of samples to be in cluster This

References MMSD_Cluster::computeMultivariateDensity(), LAP_Vector< T >::getValues(), and LAP_Vector< T >::setSize().

Here is the call graph for this function:

static tString CORE_Object::getClassName ( const tString & identityString )

inlinestaticinherited

return the class name of the object using only the identity string

Referenced by UI_Class::createVector2D(), LAP_DoublePackedUpperMatrix::matrixProduct(), LAP_DoubleBandedUpperMatrix::matrixProduct(), LAP_DoubleFullUpperMatrix::matrixProduct(), and CORE_Object::printObjectsInMemory().

Here is the caller graph for this function:

tString CORE_Object::getClassName ( ) const

inherited

return the class name of the object

Returns: the class name of the object

References tString.

Referenced by CORE_Object::getIdentityString().

Here is the caller graph for this function:

const MMSD_DoubleVector& MMSD_Cluster::getFreedomDegrees ( ) const

inlineinherited

get the freedom degree of property of size P

MMSD_GaussianFDFunction& MMSD_GaussianCluster::getFunction ( )

inlineprotectedinherited

get the function to find zero

Referenced by updateFreedomDegrees(), and MMSD_GaussianCluster::updateFreedomDegrees().

Here is the caller graph for this function:

tString CORE_Object::getIdentityString ( ) const

inlineinherited

return the identity string of the object of the form className_at_address

Returns: the identity string of the object

References CORE_Object::getClassName(), CORE_Object::pointer2String(), and tString.

Referenced by UI_Class::createPrimitiveMap(), UI_Class::saveAssociation(), UI_Class::saveClass(), UI_ClassFactory::saveIntoClass(), MATH_StiefelFunction::toString(), LAP_2DView::toString(), CORE_Object::toString(), MATH_StiefelOptimizer::toString(), and MM_Class::toString().

Here is the call graph for this function:

Here is the caller graph for this function:

const MMSD_Law* MMSD_Cluster::getLaw ( ) const

inlineinherited

get the law

double MMSD_Cluster::getMaxFreedomDegreeValue ( ) const

inlineinherited

get the max freedom degree value

Referenced by MMSD_GaussianCluster::MMSD_GaussianCluster().

Here is the caller graph for this function:

static ostream& CORE_Object::getOutput ( )

inlinestaticinherited

get output

tString CORE_Object::getPointerAddress ( ) const

inlineinherited

return the identity string of the object

Returns: the identity string of the object

References CORE_Object::pointer2String().

Here is the call graph for this function:

double MMSD_Cluster::getRate ( ) const

inlineinherited

get rate of the cluster which is the percent of samples in this cluster.

Referenced by MMSD_Model::computeSampleClusterProbabilities().

Here is the caller graph for this function:

void CORE_Object::getSharedPointer ( SP::CORE_Object & p )

inlineinherited

get the shared pointer of this class into p

Referenced by CORE_Map< Key, Value >::getSharedPointer(), CORE_Array< tFlag >::getSharedPointer(), LAP_ConstVector< lapack_real >::getSharedPointer(), STAT_Combinatorial< T >::getSharedPointer(), LAP_Vector< lapack_int >::getSharedPointer(), CORE_Vector< T >::getSharedPointer(), CORE_Matrix< T >::getSharedPointer(), and CORE_Object::printObjectsInMemory().

Here is the caller graph for this function:

void CORE_Object::getSharedPointer ( SPC::CORE_Object & p ) const

inlineinherited

get the shared pointer of this class into p

MATH_Equation& MMSD_GaussianCluster::getSolver ( )

inlineprotectedinherited

get the solver

Referenced by updateFreedomDegrees(), and MMSD_GaussianCluster::updateFreedomDegrees().

Here is the caller graph for this function:

template<class T >

static tString CORE_Object::getTypeName ( )

inlinestaticinherited

get type name

References tString.

const MMSD_DoubleFullMatrix& MMSD_Cluster::getWeights ( ) const

inlineinherited

get the weight of sample 's property of size NxP

tBoolean UI_Object::hasBeenLoaded ( ) const

inlineinherited

return true if the object has completely been loaded

Referenced by UI_Class::loadAssociation().

Here is the caller graph for this function:

void MMSD_Cluster::initialize	(	const int &	clusterIndex,
		const MMSD_IntegerVector &	clusterIndexSamples,
		const MMSD_DoubleFullMatrix &	properties
	)

virtualinherited

initialize the cluster

Parameters

clusterIndex	index of the cluster This
clusters	: clusters index of size N for each samples
properties	matrix Y of properties of size N x P

updates the rate (mRate) of the cluster (number of samples in cluster clusterIndex / N)
updates empty attribute of the cluster (mRate==0)
creates the law & initialize it ( see MMD_Law::initialize() )
creates & initializes freedom degree parameters of size P & set to 20 by default
creates & initializes weights of size NxP depending on weight initialization parameters (see MMSD_Cluster::setWeightInitializationType()

References LAP_DoubleFullGeneralMatrix::getColumnsNumber(), LAP_DoubleFullGeneralMatrix::getRowsNumber(), LAP_DoubleMatrix::getStorage(), LAP_DoubleMatrixStorage::getValues(), LAP_Vector< T >::getValues(), STAT_GammaDistribution::New(), null, LAP_DoubleFullGeneralMatrix::setSize(), and LAP_Vector< T >::setSize().

Here is the call graph for this function:

void MMSD_Object::initSeed ( const long int & v )

staticinherited

init the seed with v value

References STAT_Distribution::initSeed().

Here is the call graph for this function:

void MMSD_Object::initSeed ( )

staticinherited

init the seed

References CORE_Time::getTime().

Referenced by MMSD_Object::MMSD_Object(), testGaussianLaw11N(), testGaussianLaw1PN(), and testGaussianLaw2PN().

Here is the call graph for this function:

Here is the caller graph for this function:

static tBoolean CORE_Object::is32Architecture ( )

inlinestaticinherited

return true if the machine is a 32 bits machine

References CORE_Object::is64Architecture().

Here is the call graph for this function:

tBoolean CORE_Object::is64Architecture ( )

staticinherited

return true if the machine is a 64 bits machine

Referenced by CORE_Object::is32Architecture().

Here is the caller graph for this function:

tBoolean MMSD_Cluster::isEmpty ( ) const

inlineinherited

return true is the cluster is empty

Referenced by MMSD_Model::esperanceEvaluation().

Here is the caller graph for this function:

template<class T >

tBoolean CORE_Object::isInstanceOf ( ) const

inlineinherited

return true if the object is an instance of T

References null.

void MMSD_Cluster::loadFromUIClass ( const UI_Class & mclass )

protectedvirtualinherited

how to load the object from a Meta Model class

Reimplemented from UI_Object.

References UI_Class::getInterfaceType(), UI_Class::loadAssociation(), UI_Class::loadField(), UI_Class::loadFullMatrixField(), LAP_DoubleFullGeneralMatrix::setValues(), LAP_Vector< T >::setValues(), and tBoolean.

Here is the call graph for this function:

static SP::MMSD_ConstraintGaussianCluster MMSD_ConstraintGaussianCluster::New ( )

inlinestatic

create an instance of gaussian law

References MMSD_ConstraintGaussianCluster().

Referenced by MMSD_ConstraintGaussianModel::NewClusterInstance().

Here is the call graph for this function:

Here is the caller graph for this function:

void CORE_Object::outputPrint ( const tString & message )

staticinherited

print on output

References null, and CORE_Object::print().

Referenced by CORE_Exception::CORE_Exception().

Here is the call graph for this function:

Here is the caller graph for this function:

tString CORE_Object::pointer2String ( const void * obj )

staticinherited

return the string represantation of a pointer

References tString.

Referenced by CORE_Object::CORE_Object(), CORE_Object::getIdentityString(), CORE_Object::getPointerAddress(), and CORE_Object::~CORE_Object().

Here is the caller graph for this function:

virtual void CORE_Object::print ( )

inlinevirtualinherited

print the class

References CORE_Object::toString().

Referenced by CORE_Object::outputPrint(), CORE_Out::print(), CORE_Object::print(), CORE_Out::printInt(), CORE_Out::println(), CORE_Out::printReal(), CORE_Out::printString(), and CORE_Out::setAction().

Here is the call graph for this function:

Here is the caller graph for this function:

virtual ostream& CORE_Object::print ( ostream & out ) const

inlinevirtualinherited

print the class

References CORE_Object::print(), and CORE_Object::toString().

Here is the call graph for this function:

void CORE_Object::print ( const tString & message )

virtualinherited

print the class

Reimplemented in CORE_Out.

References null, and CORE_Object::print().

Here is the call graph for this function:

void CORE_Object::print ( const tInteger & str )

virtualinherited

print

References null.

void CORE_Object::print ( const tRelativeInteger & str )

virtualinherited

print

References null.

void CORE_Object::print ( const tReal & str )

virtualinherited

print

References null.

void CORE_Object::print ( const int & str )

virtualinherited

print

References null.

static ostream& CORE_Object::print	(	ostream &	out,
		const tString &	message
	)

inlinestaticinherited

print the class

void CORE_Object::printObjectsInMemory ( )

staticinherited

print object in memory

References CORE_Object::getClassName(), CORE_Object::getSharedPointer(), and CORE_Object::mIsMemoryTesting.

Referenced by main().

Here is the call graph for this function:

Here is the caller graph for this function:

void MMSD_Cluster::restore ( const MMSD_DoubleFullMatrix & properties )

virtualinherited

restore the unstored values after a backup

restores its law see MMSD_Law::restore()
updates empty attribute of the cluster (mRate==0)

void MMSD_Cluster::saveToUIClass ( UI_Class & mclass ) const

protectedvirtualinherited

how to save the object from a mate model class

Reimplemented from UI_Object.

References LAP_DoubleFullGeneralMatrix::getColumnsNumber(), UI_Class::getInterfaceType(), LAP_DoubleFullGeneralMatrix::getRowsNumber(), LAP_Vector< T >::getSize(), LAP_DoubleMatrix::getStorage(), LAP_DoubleMatrixStorage::getValues(), LAP_Vector< T >::getValues(), UI_Class::saveAssociation(), UI_Class::saveField(), and UI_Class::saveFullMatrixField().

Here is the call graph for this function:

void UI_Object::setHasBeenLoaded ( const tBoolean & v )

inlineinherited

set the if the object has completely been loaded

Referenced by UI_Class::loadAssociation().

Here is the caller graph for this function:

void MMSD_Cluster::setLaw ( SP::MMSD_Law law )

inlineinherited

set the law

void MMSD_Cluster::setMaxFreedomDegreeValue ( const double & v )

inlineinherited

set the max freedom degree value

Parameters

v	max freedom value

By default set to 299

static void CORE_Object::setOutput ( ostream & out )

inlinestaticinherited

set output

void CORE_Object::setThis ( SP::CORE_Object p )

inlineprotectedinherited

set this weak shared pointer called toDoAfterThis setting method

References CORE_Object::toDoAfterThisSetting().

Here is the call graph for this function:

virtual void CORE_Object::setType ( tString type )

inlineprotectedvirtualinherited

set the type of the object

Here is the caller graph for this function:

void MMSD_Cluster::setWeightInitializationType	(	const tString &	type,
		const double &	shape,
		const double &	rate
	)

inlineinherited

set the weight initialization type

Parameters

type	of weight initialization ["gamma" or "constant"]
shape	: parameter for statistic function weight initialization
rate	: parameter for statistic function weight initialization

References CORE_String::toLower(), and tString.

Referenced by MMSD_Cluster::setWeightInitializationType().

Here is the call graph for this function:

Here is the caller graph for this function:

void MMSD_Cluster::setWeightInitializationType	(	const tFlag &	t,
		const double &	shape,
		const double &	rate
	)

inlineinherited

set the weight initialization type

Parameters

type	of weight initialization MMSD_Cluster::GAMMA_WEIGHT_INITIALIZATION, MMSD_Cluster::CONSTANT_WEIGHT_INITIALIZATION
shape	: parameter for statistic function weight initialization
rate	: parameter for statistic function weight initialization

void MMSD_Cluster::setWeightInitializationType ( const tFlag & t )

inlineinherited

set the weight initialization type

Parameters

type	of weight initialization MMSD_Cluster::GAMMA_WEIGHT_INITIALIZATION, MMSD_Cluster::CONSTANT_WEIGHT_INITIALIZATION

References MMSD_Cluster::setWeightInitializationType().

Here is the call graph for this function:

void MMSD_Cluster::sort ( )

inlineinherited

sort the freedom degrees with respect to the law

Referenced by MMSD_Model::esperanceMaximization().

Here is the caller graph for this function:

virtual void CORE_Object::toDoAfterThisSetting ( )

inlineprotectedvirtualinherited

method called after setThis() method this method can oly be called once.

Reimplemented in STAT_UniformLaplaceTransform.

Referenced by CORE_Object::setThis(), and STAT_UniformLaplaceTransform::toDoAfterThisSetting().

Here is the caller graph for this function:

virtual tString MMSD_ConstraintGaussianCluster::toString ( ) const

inlinevirtual

turn the class into string

Reimplemented from MMSD_GaussianCluster.

References MMSD_GaussianCluster::toString(), and tString.

Here is the call graph for this function:

void MMSD_ConstraintGaussianCluster::updateFreedomDegrees	(	const MMSD_DoubleFullMatrix &	W,
		const MMSD_DoubleVector &	probs,
		const double &	maxFD,
		MMSD_DoubleVector &	nus
	)

protectedvirtual

update the freedom degrees from weights & probabilities.

Parameters

W	weights of the cluster of size NxP
probs	: probability of each sample to be in This cluster of size N
maxFD	max value of freedom degrees see MMSD_Cluster::setMaxFreedomDegreeValue()
nus	value of freedom degree of size P

nu=nus[0] max bounded by maxFreedomDegreeValue
t=(nu+1)/2
s=0
for j in [0,P[
- sp=0
- for i in [0,N[
- sP+=probs[i]
- s+= probs[i]*(log(W[i][j])-W[i][j])
- solve F(sP,s,t)(nu)=0 for nu0=nu
for j in [O,P[
- nus[j]=nu;

(see MMSD_GaussianFDFunction::compute() && MATH_Equation::solve() )

Reimplemented from MMSD_GaussianCluster.

References MMSD_GaussianCluster::getFunction(), LAP_Vector< T >::getSize(), MMSD_GaussianCluster::getSolver(), LAP_DoubleMatrix::getStorage(), LAP_DoubleMatrixStorage::getValues(), LAP_Vector< T >::getValues(), null, MMSD_GaussianFDFunction::setParameters(), MATH_Equation::solve(), and LAP_DoubleVector::sum().

Here is the call graph for this function:

void MMSD_Cluster::updateFreedomDegrees ( const MMSD_DoubleVector & probs )

inlineinherited

update the freedom degrees

Referenced by MMSD_Model::esperanceMaximization().

Here is the caller graph for this function:

void MMSD_Cluster::updateLaw	(	const MMSD_DoubleFullMatrix &	properties,
		const MMSD_DoubleVector &	probs
	)

inlineinherited

update the law parameters

Referenced by MMSD_Model::esperanceMaximization().

Here is the caller graph for this function:

void MMSD_Cluster::updateRate ( const MMSD_DoubleVector & clusterProbabilitiesSamples )

inherited

update the rate of the cluster

Parameters

clusterProbabilitiesSamples probability of each sample to be in this cluster

References LAP_Vector< T >::getSize(), and LAP_Vector< T >::getValues().

Referenced by MMSD_Model::esperanceEvaluation().

Here is the call graph for this function:

Here is the caller graph for this function:

void MMSD_GaussianCluster::updateWeights	(	const MMSD_DoubleFullMatrix &	YP,
		const MMSD_DoubleFullMatrix &	P,
		const MMSD_DoubleVector &	Diag,
		const MMSD_DoubleVector &	mean,
		const MMSD_DoubleVector &	nus,
		const MMSD_DoubleVector &	probs,
		MMSD_DoubleFullMatrix &	W
	)		const

protectedvirtualinherited

compute the weights from law, freedom degrees & probabilites

Parameters

YP	: Y.P matrix of size NxP
P	: P eigen value decomposition matrix of cov(Y) of size PXP
D	: D eigen value decomposition diagonal matrix of cov(Y) of size P
mean	: mean value of the properties cluster of size P
nu	: freedom degrees of the cluster of size P
probs	: probability of the sample i in(0,N[ to be in the cluster This.
W	: output weight matrix of size NxP