source: trunk/yat/utility/PCA.cc @ 1028

// $Id: PCA.cc 1028 2008-02-03 01:53:29Z peter $

/*
  Copyright (C) 2003 Daniel Dalevi
  Copyright (C) 2004 Jari Häkkinen
  Copyright (C) 2005 Jari Häkkinen, Peter Johansson
  Copyright (C) 2006 Jari Häkkinen
  Copyright (C) 2007 Jari Häkkinen, Peter Johansson

  This file is part of the yat library, http://trac.thep.lu.se/yat

  The yat library is free software; you can redistribute it and/or
  modify it under the terms of the GNU General Public License as
  published by the Free Software Foundation; either version 2 of the
  License, or (at your option) any later version.

  The yat library is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
  General Public License for more details.

  You should have received a copy of the GNU General Public License
  along with this program; if not, write to the Free Software
  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
  02111-1307, USA.
*/

#include "PCA.h"
#include "SVD.h"
#include "utility.h"
#include "VectorView.h"

#include <iostream>
#include <cmath>
#include <memory>

namespace theplu {
namespace yat {
namespace utility {


  PCA::PCA(const utility::matrix& A)
    : A_(A)
  {
    process();
  }


  const utility::vector& PCA::eigenvalues(void) const
  {
    return eigenvalues_;
  }


  const utility::matrix& PCA::eigenvectors(void) const
  {
    return eigenvectors_;
  }


  void PCA::process(void)
  {
    // Row-center the data matrix
    utility::matrix A_center( A_.rows(), A_.columns() );
    this->row_center( A_center );

    // Single value decompose the data matrix
    std::auto_ptr<SVD> pSVD( new SVD( A_center ) );
    pSVD->decompose();
    utility::matrix U(pSVD->U());
    utility::matrix V(pSVD->V());

    // Read the eigenvectors and eigenvalues
    eigenvectors_.clone(U);
    eigenvectors_ .transpose();
    eigenvalues_ = pSVD->s();

    // T
    for( size_t i = 0; i < eigenvalues_.size(); ++i )
      eigenvalues_(i) = eigenvalues_(i)*eigenvalues_(i);
    eigenvalues_ *= 1.0/A_center.rows();

    // Sort the eigenvectors in order of eigenvalues
    // Simple (not efficient) algorithm that always 
    // make sure that the i:th element is in its correct 
    // position (N element --> Ordo( N*N ))
    for ( size_t i = 0; i < eigenvalues_.size(); ++i )
      for ( size_t j = i + 1; j < eigenvalues_.size(); ++j )
        if ( eigenvalues_(j) > eigenvalues_(i) ) {
          std::swap( eigenvalues_(i), eigenvalues_(j) ); 
          eigenvectors_.swap_rows(i,j);
        }
  }


  /*
  void PCA::process_transposed_problem(void)
  {
    // Row-center the data matrix
    utility::matrix A_center( A_.rows(), A_.columns() );
    this->row_center( A_center );

    // Transform into SVD friendly dimension
    A_.transpose();
    A_center.transpose();

    // Single value decompose the data matrix
    std::auto_ptr<SVD> pSVD( new SVD( A_center ) );
    pSVD->decompose();
    utility::matrix U(pSVD->U());
    utility::matrix V(pSVD->V());

    // Read the eigenvectors and eigenvalues
    eigenvectors_.clone(V);
    eigenvectors_.transpose();
    eigenvalues_.clone(pSVD->s());

    // Transform back when done with SVD!
    // (used V insted of U now for eigenvectors)
    A_.transpose();
    A_center.transpose();

    // T
    for( size_t i = 0; i < eigenvalues_.size(); ++i )
      eigenvalues_[ i ] = eigenvalues_[ i ]*eigenvalues_[ i ];
    eigenvalues_ *= 1.0/A_center.rows();

    // Sort the eigenvectors in order of eigenvalues
    // Simple (not efficient) algorithm that always 
    // make sure that the i:th element is in its correct 
    // position (N element --> Ordo( N*N ))
    for ( size_t i = 0; i < eigenvalues_.size(); ++i )
      for ( size_t j = i + 1; j < eigenvalues_.size(); ++j )
        if ( eigenvalues_[ j ] > eigenvalues_[ i ] ) {
          std::swap( eigenvalues_[ i ], eigenvalues_[ j ] ); 
          eigenvectors_.swap_rows(i,j);
        }
  }
  */


  utility::matrix PCA::projection(const utility::matrix& samples ) const
  {
    const size_t Ncol = samples.columns();
    const size_t Nrow = samples.rows();
    utility::matrix projs( Ncol, Ncol );

    utility::vector temp(samples.rows());
    for( size_t j = 0; j < Ncol; ++j ) {
      for (size_t i=0; i<Ncol; ++i )
        temp(i) = samples(i,j); 
      utility::vector centered( Nrow );
      for( size_t i = 0; i < Nrow; ++i ) 
        centered(i) = temp(i) - meanvalues_(i);
      utility::vector proj( eigenvectors_ * centered );
      for( size_t i = 0; i < Ncol; ++i ) 
        projs(i,j)=proj(i);
    }
    return projs;
  }


  /*
  utility::matrix
  PCA::projection_transposed(const utility::matrix& samples) const
  {
    const size_t Ncol = samples.columns();
    const size_t Nrow = samples.rows();
    utility::matrix projs( Nrow, Ncol );

    utility::vector temp(samples.rows());
    for( size_t j = 0; j < Ncol; ++j ) {
      for (size_t i=0; i<Ncol; ++i )
        temp(i) = samples(i,j); 
      utility::vector centered( Nrow );
      for( size_t i = 0; i < Nrow; ++i ) 
        centered(i)=temp(i)-meanvalues_(i);
      utility::vector proj( eigenvectors_ * centered );
      for( size_t i = 0; i < Nrow; ++i ) 
        projs(i,j)=proj(i);
    }
    return projs;
  }
  */


  // This function will row-center the matrix A_,
  // that is, A_ = A_ - M, where M is a matrix
  // with the meanvalues of each row
  void PCA::row_center(utility::matrix& A_center)
  {
    meanvalues_ = vector(A_.rows());
    utility::vector A_row_sum(A_.rows());
    for (size_t i=0; i<A_row_sum.size(); ++i){
      A_row_sum(i) = sum(A_.row_const_view(i));
    }
    for( size_t i = 0; i < A_center.rows(); ++i ) {
      meanvalues_(i) = A_row_sum(i) / static_cast<double>(A_.columns());
      for( size_t j = 0; j < A_center.columns(); ++j )
        A_center(i,j) = A_(i,j) - meanvalues_(i);
    }
  }

}}} // of namespace utility, yat, and theplu