A Linear AutoAssociative Model (LAAM) is a generalization of the PCA model for projecting variables on an affine plane of lower dimension. More...

#include <STK_LinearAAModel.h>

Inheritance diagram for STK::LinearAAModel< Array >:

Public Types
typedef IRunnerUnsupervised< Array, VectorX >	Runner

typedef GaussianAAModel< Array >	Base

Public Types inherited from STK::GaussianAAModel< Array >
typedef IStatModel< GaussianAAModel< Array > >	Base

Public Types inherited from STK::IStatModel< GaussianAAModel< Array > >
typedef hidden::ModelTraits< GaussianAAModel< Array > >::Data	Data

typedef hidden::ModelTraits< GaussianAAModel< Array > >::ParamHandler	ParamHandler

typedef Data::Type	Type
	Type of the data contained in the container.

typedef hidden::Traits< Data >::Row	Row
	Type of the row of the data container (a sample)

Public Member Functions
	LinearAAModel (Array const &data)
	constructor.

	LinearAAModel (LinearAAModel const &model)
	copy constructor.

virtual	~LinearAAModel ()
	Virtual destructor.

virtual LinearAAModel *	clone () const
	clone pattern

bool	run (int const &dim)
	run the estimation of the AA model.

bool	run (VectorX const &weights, int const &dim)
	run the estimation of the weighted AA model.

virtual bool	run ()
	run the estimation of the AA model.

virtual bool	run (VectorX const &weights)
	run the estimation of the weighted AA model.

Public Member Functions inherited from STK::IRunnerUnsupervised< Array, VectorX >
Array const *	p_data () const
	get the data set

virtual void	setData (Array const *p_data)
	Set the data set.

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

Public Member Functions inherited from STK::IRunnerBase
String const &	error () const
	get the last error message.

Public Member Functions inherited from STK::GaussianAAModel< Array >
	GaussianAAModel (Array *p_workData)
	Constructor.

	GaussianAAModel (Array &workData)
	Constructor.

virtual	~GaussianAAModel ()
	virtual destuctor.

Real const &	projectedLnLikelihood () const

Real const &	residualLnLikelihood () const

ArraySquareX const &	projectedCovariance () const

ArraySquareX const &	residualCovariance () const

Real const &	residualVariance () const

virtual void	setWorkData (Array &workData)
	Set a new working data set.

void	computeProjectedCovariance ()
	compute the covariance matrix of the projected data set.

void	computeModelParameters ()
	compute the ln-likelihood of the model

Public Member Functions inherited from STK::IAAModel< Array >
	~IAAModel ()
	destructor.

Array const &	workData () const

Reducer *const &	p_reducer () const

Regressor *const &	p_regressor () const

Array *const &	p_reduced () const

Array *const &	p_predicted () const

Array *const &	p_residuals () const

int	dim () const

bool	isCentered () const

bool	isStandardized () const

PointX const &	mean () const

PointX const &	std () const

void	setDimension (int const &dim)

void	setWorkData (Array &workData)

void	setReducer (Reducer *p_reducer)

void	setRegressor (Regressor *p_regressor)

void	freeReducer ()
	delete the reducer set to this model by the method `setReducer`.

void	freeRegressor ()
	delete the regressor set to this model by the method `setRegressor`.

void	center ()
	center the data set workData_.

void	center (VectorX const &weights)
	weighted centering of the data set.

void	standardize ()
	standardize the data set.

void	standardize (VectorX const &weights)
	weighted standardization the data set.

void	reductionStep ()
	compute the reduction of the data set and store the result in the `p_reduced_` container.

void	reductionStep (VectorX const &weights)
	compute the weighted dimension reduction of the data set and store the result in the `p_reduced_` container.

void	regressionStep ()
	compute the regression of the original data set and set the results in `p_predicted` and `p_residuals`.

void	regressionStep (VectorX const &weights)
	compute the weighted regression of the original data set using the reduced data set as predictor and set the results in `p_predicted` and `p_residuals`.

void	uncenterResults ()
	uncenter the predicted data set.

void	unstandardizeResults ()
	unstandardize the predicted data set and the residuals.

Public Member Functions inherited from STK::IStatModel< GaussianAAModel< Array > >
	~IStatModel ()
	destructor

Data const *const	p_dataij () const

void	setData (Data const &data)
	Set the data set of the model.

void	setData (Data const *p_data)
	Set the data set of the model.

Public Member Functions inherited from STK::IStatModelBase
int	nbSample () const

Real	lnNbSample () const

int	nbVariable () const

Real	lnLikelihood () const

Real	likelihood () const

int	nbFreeParameter () const

Real	computeBIC () const

Real	computeAIC () const

Real	computeML () const

Static Public Member Functions
static void	simul (const Law::IUnivLaw< Real > &law, VectorX const &mu, Real const &std, Array &proj, Array &data)
	Simulate a centered auto-associative linear model in $\mathbb{R}^p$ of the form.

Protected Attributes
Array	workData_
	working data set;

Protected Attributes inherited from STK::IRunnerUnsupervised< Array, VectorX >
Array const *	p_data_
	A pointer on the original data set.

Protected Attributes inherited from STK::IRunnerBase
String	msg_error_
	String with the last error message.

bool	hasRun_
	`true` if run has been used, `false` otherwise

Protected Attributes inherited from STK::IAAModel< Array >
Regressor *	p_regressor_
	pointer on the regression method.

Reducer *	p_reducer_
	pointer on the reeducer.

Array *	p_workData_
	Array of the local data set.

Array *	p_reduced_
	Array of the reduced data set : the data set is shared with `p_reducer` and set when the `regression` method is call.

Array *	p_predicted_
	Array of the predicted data set: the data set is shared with `p_regressor` and set when the `regression` method is call.

Array *	p_residuals_
	Array of the residuals: the data set is shared with `p_regressor` and set when the `regression` method is call.

Protected Attributes inherited from STK::IStatModel< GaussianAAModel< Array > >
Data const *	p_dataij_
	A pointer on the original data set.

Additional Inherited Members
Protected Member Functions inherited from STK::IRunnerUnsupervised< Array, VectorX >
	IRunnerUnsupervised ()
	default constructor.

	IRunnerUnsupervised (Array const *const p_data)
	constructor with a pointer on the constant data set

	IRunnerUnsupervised (Array const &data)
	constructor with a constant reference on the data set

	IRunnerUnsupervised (IRunnerUnsupervised const &runner)
	copy constructor

	~IRunnerUnsupervised ()
	destructor

Protected Member Functions inherited from STK::IRunnerBase
	IRunnerBase ()
	default constructor

	IRunnerBase (IRunnerBase const &runner)
	copy constructor

virtual	~IRunnerBase ()
	destructor

virtual void	update ()
	update the runner.

Protected Member Functions inherited from STK::GaussianAAModel< Array >
void	computeNbFreeParameters ()
	compute the number of free parameter of the model.

void	computeResidualCovariance ()
	compute the covariance matrix of the residuals.

void	computeProjectedLnLikelihood ()
	compute the ln-likelihood of the projected data set The projected data set is assumed Gaussian with an arbitrary covariance Array.

void	computeResidualLnLikelihood ()
	compute the ln-likelihood of the projected data set.

Protected Member Functions inherited from STK::IAAModel< Array >
	IAAModel (Array *p_workData)
	Constructor.

	IAAModel (Array &workData)
	Constructor.

Protected Member Functions inherited from STK::IStatModel< GaussianAAModel< Array > >
	IStatModel (Data const &data)
	Constructor with data set.

	IStatModel (Data const *p_data)
	Constructor with a ptr on the data set.

Protected Member Functions inherited from STK::IStatModelBase
	IStatModelBase ()
	Default constructor.

	IStatModelBase (int nbSample)
	Constructor with specified dimension.

	IStatModelBase (int nbSample, int nbVariable)
	Constructor with specified dimension.

	IStatModelBase (IStatModelBase const &model)
	Copy constructor.

	~IStatModelBase ()
	destructor

void	setNbFreeParameter (int const &nbFreeParameter)
	set the number of free parameters of the model

void	setNbSample (int const &nbSample)
	set the number of samples of the model

void	setNbVariable (int const &nbVariable)
	set the number of variables of the model

void	setLnLikelihood (Real const &lnLikelihood)
	set the log-likelihood of the model

void	initialize (int nbSample, int nbVariable)
	set the dimensions of the parameters of the model

Detailed Description

template<class Array>
class STK::LinearAAModel< Array >

A Linear AutoAssociative Model (LAAM) is a generalization of the PCA model for projecting variables on an affine plane of lower dimension.

A SLAAM is a (probabilistic) model of the form

$Y = \boldsymbol{\mu} + \sum_{j=1}^{q} \mathrm{Reg}^j(C^j) + \epsilon$

in $\mathbf{R}^d$ .

$ Y $ is an input d dimensional random variable and $\epsilon$ is the residual random variable. The (generalized) principal components $C^{j}$ are real random variables estimated by a projection of the centered data on a subspace

$C^j = <a^j,Y>.$

where the $ a^j$ form an orthonormal set of vector.

The regression functions $\mathrm{Reg}^j : \mathbb{R} \rightarrow \mathbb{R}^d$ are specifics to the model.

A LAAM is an auto-associative model of the form

$\begin{eqnarray*} Y_i & = & \mu + \sum_{j=1}^{q} <a^j, Y_i - \mu> V^{j} + \epsilon_i \end{eqnarray*}$

In this implementation, the axis $ a^j $ are computed using any arbitrary derived class of Index.

The principal variables $ V^j $ are computed using least square regression. As the regression model is linear there is no necessity to use the setRegresor method. it will be created by this object.

Definition at line 95 of file STK_LinearAAModel.h.

Member Typedef Documentation

◆ Base

template<class Array >

typedef GaussianAAModel<Array> STK::LinearAAModel< Array >::Base

Definition at line 100 of file STK_LinearAAModel.h.

◆ Runner

template<class Array >

typedef IRunnerUnsupervised<Array, VectorX> STK::LinearAAModel< Array >::Runner

Definition at line 99 of file STK_LinearAAModel.h.

Constructor & Destructor Documentation

◆ LinearAAModel() [1/2]

template<class Array >

STK::LinearAAModel< Array >::LinearAAModel ( Array const & data )

constructor.

compute the Linear AA models of the matrix data using the local variance as criteria.

Parameters

data	the data set to modelize

Definition at line 204 of file STK_LinearAAModel.h.

                                   : Runner(), Base(0), workData_(data)
{
  Runner::setData(workData_);
  Base::setWorkData(workData_);
  p_regressor_ = new MultidimRegression<Array, VectorX>();
}

References STK::IAAModel< Array >::p_regressor_, STK::IRunnerUnsupervised< Array, VectorX >::setData(), STK::GaussianAAModel< Array >::setWorkData(), and STK::LinearAAModel< Array >::workData_.

◆ LinearAAModel() [2/2]

template<class Array >

STK::LinearAAModel< Array >::LinearAAModel ( LinearAAModel< Array > const & model )

copy constructor.

Parameters

model the model to copy

Definition at line 216 of file STK_LinearAAModel.h.

                                   : Runner(), Base(0), workData_(model.workData_)
{
  Runner::setData(workData_);
  Base::setWorkData(workData_);
  p_regressor_ = new MultidimRegression<Array, VectorX>();
}

References STK::IAAModel< Array >::p_regressor_, STK::IRunnerUnsupervised< Array, VectorX >::setData(), STK::GaussianAAModel< Array >::setWorkData(), and STK::LinearAAModel< Array >::workData_.

◆ ~LinearAAModel()

template<class Array >

STK::LinearAAModel< Array >::~LinearAAModel ( )

virtual

Virtual destructor.

Definition at line 228 of file STK_LinearAAModel.h.

229{ if (p_regressor_) delete p_regressor_;}

Member Function Documentation

◆ clone()

template<class Array >

virtual LinearAAModel * STK::LinearAAModel< Array >::clone ( ) const

inlinevirtual

clone pattern

Definition at line 122 of file STK_LinearAAModel.h.

122{ return new LinearAAModel(*this);}

STK::LinearAAModel::LinearAAModel

LinearAAModel(Array const &data)

constructor.

Definition STK_LinearAAModel.h:204

◆ run() [1/4]

template<class Array >

bool STK::LinearAAModel< Array >::run ( )

virtual

run the estimation of the AA model.

The behavior of the estimation is the following :

compute the projected data set and set the result in p_reduced_
regress the workData_ set using the p_reduced_ set as predictors
compute the restored data set using the AA model and set the result in the p_predicted_ container.
compute the residuals
compute the distribution of the projected data set and the residuals

The data have to be centered before running the computations.

Implements STK::IRunnerUnsupervised< Array, VectorX >.

Definition at line 247 of file STK_LinearAAModel.h.

{
  // compute AAM
  try
  {
    if (!p_reducer_)
    {
      this->msg_error_ = STKERROR_NO_ARG(LinearAAModel::run(),reducer is not set);
      return false;
    }
    if (!p_regressor_)
    {
      this->msg_error_ = STKERROR_NO_ARG(LinearAAModel::run(),regressor is not be set);
      return false;
    }
    // set p_workData to the reducer
    p_reducer_->setData(*p_workData_);
    // compute the projected data set
    reductionStep();
    // compute the projected covariance
    this->computeProjectedCovariance();
#ifdef STK_AAMODELS_VERBOSE
    stk_cout << _T("In LinearAAModel::run(), reduction done.\n");
#endif
    // set data
    p_regressor_->setY(*p_workData_);
    p_regressor_->setX(*p_reduced_);
    // compute the regression function
    regressionStep();
#ifdef STK_AAMODELS_VERBOSE
    stk_cout << _T("In LinearAAModel::run(), regression done.\n");
#endif
    this->computeModelParameters();
    // check if data have been standardized or centered
    if (this->isStandardized()) { this->unstandardizeResults();}
    else if (this->isCentered()){ this->uncenterResults();}
  }
  catch (Exception const& error)
  {
    this->msg_error_ = _T("Error in LinearAAModel::run():\nWhat: ");
    this->msg_error_ += error.error();
    return false;
  }
  return true;
}

References _T, STK::Exception::error(), STK::IRunnerBase::error(), STK::IRunnerBase::msg_error_, STK::MultidimRegression< Array, Weight >::regressionStep(), STK::LinearAAModel< Array >::run(), stk_cout, and STKERROR_NO_ARG.

Referenced by STK::LinearAAModel< Array >::run(), and STK::LinearAAModel< Array >::run().

◆ run() [2/4]

template<class Array >

bool STK::LinearAAModel< Array >::run ( int const & dim )

run the estimation of the AA model.

The behavior of the estimation is the following :

compute the projected data set and set the result in p_reduced_
regress the workData_ set using the p_reduced_ set as predictors
compute the restored data set using the AA model and set the result in the p_predicted_ container.
compute the residuals The data have to be centered before running the computations.
Parameters

dim the dimension of the AA Model

Definition at line 233 of file STK_LinearAAModel.h.

{
  this->setDimension(dim);
  bool res = run();
#ifdef STK_DEBUG
  if (!res)
  { stk_cerr << _T("An error occur.\nWhat: ") << this->error();}
#endif
  return res;
}

References _T, STK::IRunnerBase::error(), STK::IRegression< Array, Array, Weight >::run(), and stk_cerr.

◆ run() [3/4]

template<class Array >

bool STK::LinearAAModel< Array >::run ( VectorX const & weights )

virtual

run the estimation of the weighted AA model.

The behavior of the estimation is the following :

compute the projected data set and set the result in p_reduced_
regress the data set using the reduced data set as predictors
compute the restored data set using the AA model and set the result in the p_predicted_ container
compute the residuals and set them in p_residual_
compute the distribution of the projected data set and the residuals

The data have to be centered before running the computations.

Parameters

weights the container of the weights

Implements STK::IRunnerUnsupervised< Array, VectorX >.

Definition at line 301 of file STK_LinearAAModel.h.

{
  try
  {
    if (!p_reducer_) STKRUNTIME_ERROR_NO_ARG(LinearAAModel::run,reducer is not set);
    if (!p_regressor_) STKRUNTIME_ERROR_NO_ARG(LinearAAModel::run,regressor is not set);
    // set p_workData to the reducer
    p_reducer_->setData(*p_workData_);
    // compute the weighted reduced data set
    reductionStep(weights);
    // compute the projected covariance
    this->computeProjectedCovariance();
#ifdef STK_AAMODELS_VERBOSE
    stk_cout << _T("In LinearAAModel::run(weights), reduction done.\n");
#endif
    // set data
    p_regressor_->setY(*p_workData_);
    p_regressor_->setX(*p_reduced_);
    // compute the weighted regression vectors
    regressionStep(weights);
#ifdef STK_AAMODELS_VERBOSE
    stk_cout << _T("In LinearAAModel::run(weights), regression done.\n");
#endif
    this->computeModelParameters();
    // check if data have been standardized or centered
    if (this->isStandardized()) { this->unstandardizeResults();}
    else if (this->isCentered()){ this->uncenterResults();}
  }
  catch (Exception const& error)
  {
    this->msg_error_ = _T("Error in LinearAAModel::run(weights): ");
    this->msg_error_ += error.error();
    return false;
  }
  return true;
}

References _T, STK::Exception::error(), STK::IRunnerBase::error(), STK::IRunnerBase::msg_error_, STK::MultidimRegression< Array, Weight >::regressionStep(), STK::LinearAAModel< Array >::run(), stk_cout, and STKRUNTIME_ERROR_NO_ARG.

◆ run() [4/4]

template<class Array >

bool STK::LinearAAModel< Array >::run	(	VectorX const &	weights,
		int const &	dim
	)

run the estimation of the weighted AA model.

The behavior of the estimation is the following :

compute the projected data set and set the result in p_reduced_
regress the data set using the reduced data set as predictors
compute the restored data set using the AA model and set the result in the p_predicted_ container
compute the residuals and set them in p_residual_

The data have to be centered before running the computations.

Parameters

dim	the dimension of the AA Model
weights	the container of the weights

Definition at line 295 of file STK_LinearAAModel.h.

{
  this->setDimension(dim);
  return run(weights);
}

References STK::IRegression< Array, Array, Weight >::run().

◆ simul()

template<class Array >

void STK::LinearAAModel< Array >::simul	(	const Law::IUnivLaw< Real > &	law,
		VectorX const &	mu,
		Real const &	std,
		Array &	proj,
		Array &	data
	)

static

Simulate a centered auto-associative linear model in $\mathbb{R}^p$ of the form.

$X = X.P.P' + \epsilon$

with $ P'P = I_d $ and d < p.

Parameters

law	the law to use in order to simulate the data.
mu	the position parameter of the AA model
std	the standard deviation of the gaussian noise
proj	the simulated projection matrix. The dimension of the container give the dimension of the AA model.
data	the data to simulate. The dimension of the container give the number of the samples and variables.

Definition at line 351 of file STK_LinearAAModel.h.

{
  if (data.cols() != mu.range())
    STKRUNTIME_ERROR_NO_ARG(LinearAAModel::simul,data.cols()!=mu.range());
  // simul AA model
  data.rand(law);
#ifdef STK_AAMODELS_VERBOSE
  stk_cout << _T("data simulated\n");
#endif
  // choose arbitrary coefficients for proj
  proj.randGauss();
#ifdef STK_AAMODELS_VERBOSE
  stk_cout << _T("proj simulated\n");
#endif
  // orthonormalize proj
  gramSchmidt(proj);
#ifdef STK_AAMODELS_VERBOSE
  stk_cout << _T("proj orthonormalized\n");
#endif
 
#ifdef STK_AAMODELS_DEBUG
  stk_cout << _T("proj =") << proj;
#endif
  // compute data
  data = data * (proj * proj.transpose());
 
  // add noise to the model
  for (int j= data.beginCols(); j< data.endCols(); j++)
  {
    Law::Normal noise(mu[j], std);
    for (int i= data.beginRows(); i< data.endRows(); i++)
      data(i, j) += noise.rand();
  }
}

References _T, STK::gramSchmidt(), STK::LinearAAModel< Array >::simul(), stk_cout, and STKRUNTIME_ERROR_NO_ARG.

Referenced by STK::LinearAAModel< Array >::simul().

Member Data Documentation

◆ workData_

template<class Array >

Array STK::LinearAAModel< Array >::workData_

protected

working data set;

Definition at line 196 of file STK_LinearAAModel.h.

Referenced by STK::LinearAAModel< Array >::LinearAAModel(), and STK::LinearAAModel< Array >::LinearAAModel().

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

STK_LinearAAModel.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Base

◆ Runner

Constructor & Destructor Documentation

◆ LinearAAModel() [1/2]

◆ LinearAAModel() [2/2]

◆ ~LinearAAModel()

Member Function Documentation

◆ clone()

◆ run() [1/4]

◆ run() [2/4]

◆ run() [3/4]

◆ run() [4/4]

◆ simul()

Member Data Documentation

◆ workData_