STK::PcaModel Class Reference

A Principal Component Analysis is a Singular Value Decomposition of the original data. More...

#include <STK_PcaModel.h>

Inherits STK::SemiLinearAAModel.

List of all members.

Public Member Functions
	PcaModel (Matrix const &X=Matrix(), bool ref=false)
	PcaModel (Matrix const &X, Vector const &W, bool ref=false)
	PcaModel (const PcaModel &mod)
virtual	~PcaModel ()
void	clear ()
virtual void	run ()
void	step ()
PcaModel &	operator= (const PcaModel &mod)
Private Member Functions
void	pca ()

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Detailed Description

A Principal Component Analysis is a Singular Value Decomposition of the original data.

• The PcaModel class derive from the SemiLinearAAModel Class.
• The observation should not have NA values.
• The container SemiLinearAAModel::criteria_, contain the cumulated inertia.

Definition at line 56 of file STK_PcaModel.h.

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Constructor & Destructor Documentation

STK::PcaModel::PcaModel	(	Matrix const &	X = Matrix(),
		bool	ref = false
	)

Default ctor. Compute the PCA with of the observations stored in the matrix X.

Definition at line 55 of file STK_PcaModel.cpp.

                  : SemiLinearAAModel(X, ref)
{
  // If there is no data : the PcaModel Model is computed

STK::PcaModel::PcaModel	(	Matrix const &	X,
		Vector const &	W,
		bool	ref = false
	)

Misc ctor. Compute the weighted PCA of the observations stored in the matrix X.

Definition at line 67 of file STK_PcaModel.cpp.

                  : SemiLinearAAModel(X, W, ref)
{
  // copy X_ in comp_
  this->comp_ = this->X_;

  // If there is no data : the PcaModel Model is computed

STK::PcaModel::PcaModel

(

const PcaModel &

mod

)

Copy ctor.

Definition at line 82 of file STK_PcaModel.cpp.

STK::PcaModel::~PcaModel

(

)

[virtual]

Virtual destructor

Definition at line 86 of file STK_PcaModel.cpp.

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Member Function Documentation

void STK::PcaModel::clear

(

)

clear all storage.

Definition at line 90 of file STK_PcaModel.cpp.

void STK::PcaModel::run

(

)

[virtual]

Compute the PCA of X Without effect if compModel_ == true (the computation is already done).

Definition at line 97 of file STK_PcaModel.cpp.

References pca().

Referenced by step().

{
  if (!this->compModel_)      // model has not been computed
  { pca();                    // compute the pca model
    this->compModel_ = true;  // computation done

void STK::PcaModel::step

(

)

[inline]

Compute a step of the the PCA of X Without effect if compModel_ == true (the computation is already done).

Definition at line 94 of file STK_PcaModel.h.

References run().

{ run();}

PcaModel & STK::PcaModel::operator=

(

const PcaModel &

mod

)

Operator = : overwrite the PcaModel with P.

Definition at line 106 of file STK_PcaModel.cpp.

              : overwrite the PcaModel with P.                     */
PcaModel& PcaModel::operator=(const PcaModel &mod)
{       SemiLinearAAModel *p1;        // pointer on this
  const SemiLinearAAModel *p2;        // pointer on mod
  p1 = this;        // conversion to SemiLinearAAModel class
  p2 = &mod;        // idem for mod
  (*p1) = (*p2);        // copy SemiLinearAAModel part
     

void STK::PcaModel::pca

(

)

[private]

compute the pca, calling compSvd(). Construct the biplot : scale U_ in oder to obtain the components.

Definition at line 120 of file STK_PcaModel.cpp.

References STK::abs(), STK::Svd::getD(), STK::Svd::getV(), and STK::Svd::rank().

Referenced by run().

{
  // copy X_ in comp_
  this->comp_ = this->X_;
  // save currrent beginning
  Integer cbeg = comp_.firstCol(), rbeg = comp_.firstRow();
  // if there is weights, pre-mult of comp_ by W^{1/2}
  if (this->weighted_)
    for (Integer i=cbeg; i<=comp_.lastCol(); i++)
      this->comp_(i) *= sqrt(abs(this->W_.at(i)));
  // compute the svd of comp_, the result will be in comp_
  // thus ref = true
  comp_.shift(); // set newbeg to (1,1) : needed by Svd
  // create a svd of comp_
  Svd *csvd = new Svd(this->comp_, true);

  // get the number of components
  this->ncomp_ = csvd->rank();
  // delete unecessary cols of comp_
  this->comp_.popBackCols(this->nvar_ - this->ncomp_);
  // get the std of the Components (the singular values)
  this->cstd_.swap(csvd->getD());
  this->cstd_.popBack(this->nvar_ - this->ncomp_);
  // get the Axis
  this->axis_.swap(csvd->getV());
  this->axis_.popBackCols(this->nvar_ - this->ncomp_);

  // clear csvd
  delete csvd;

  // restore beginning
  comp_.shift(rbeg, cbeg);
  cstd_.shift(cbeg);
  axis_.shift(rbeg, cbeg);
  
  // if there is weights, post-mult of comp_ by W^{-1/2}
  if (this->weighted_)
    for (Integer i=rbeg; i<=comp_.lastRow(); i++)
    { Real weight = sqrt(abs(this->W_.at(i)));
      // divide the ith row by weight
      if (weight) this->comp_(i) /= weight;
    }
  else
  { // compute the components and its standard deviation
    const Real aux = sqrt(this->nobs_);
    for (Integer i=cbeg; i<=comp_.lastCol(); i++)
    {
      comp_[i] *= this->cstd_[i]/ aux;
    }
  }
  // Compute the variance of comp_ = criteria_
  this->cvar_.resize(comp_.rangeHo());
  this->criteria_.resize(comp_.rangeHo());
  for (Integer j=comp_.firstCol(); j<=comp_.lastCol(); j++)
  {
    this->cvar_[j] = this->cstd_[j] * this->cstd_[j];
    this->criteria_[j] = this->cvar_[j];

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

• STK_PcaModel.h
• STK_PcaModel.cpp