PrincipalComponentAnalysis.cpp

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#include <QString>

#include "PrincipalComponentAnalysis.h"
#include "jama/jama_eig.h"
#include "jama/jama_lu.h"

using namespace std;

namespace Isis {
  PrincipalComponentAnalysis::PrincipalComponentAnalysis(const int n) {
    p_dimensions = n;
    p_statistics.clear();
    p_statistics.resize(n * n);
    for(int i = 0; i < n; i++) {
      for(int j = 0; j <= i; j++) {
        p_statistics[n*i+j] = new Isis::MultivariateStatistics();
        p_statistics[n*j+i] = p_statistics[n*i+j];
      }
    }

    p_hasTransform = false;
  };

  // create a pca object from the trabsform matrix
  PrincipalComponentAnalysis::PrincipalComponentAnalysis(TNT::Array2D<double> transform) {
    if(transform.dim1() != transform.dim2()) {
      std::string m = "Illegal transform matrix";
      throw IException(IException::Programmer, m, _FILEINFO_);
    }

    p_dimensions = transform.dim1();
    p_transform = transform;
    ComputeInverse();

    p_hasTransform = true;
  }

  // Add data for all dimensions
  //  Note: the data should be stored as an array containing
  //   the first dimension in order, then the second, ...
  void PrincipalComponentAnalysis::AddData(const double *data, const unsigned int count) {
    // If this PCA object has a transform matrix
    //  we cannot add more data
    if(p_hasTransform) {
      std::string m = "Cannot add data to a PCA that has a defined transform matrix";
      throw IException(IException::Programmer, m, _FILEINFO_);
    }

    // add the data to the multivariate stats objects
    for(int i = 0; i < p_dimensions; i++) {
      for(int j = 0; j <= i; j++) {
        p_statistics[p_dimensions*i+j]->AddData(&data[count*i], &data[count*j], count);
      }
    }
  }

  // Use VDV' decomposition to obtain the eigenvectors
  void PrincipalComponentAnalysis::ComputeTransform() {
    if(p_hasTransform) {
      std::string m = "This PCA already has a computed transform";
      throw IException(IException::Programmer, m, _FILEINFO_);
    }

    TNT::Array2D<double> C(p_dimensions, p_dimensions);
    for(int i = 0; i < p_dimensions; i++) {
      for(int j = 0; j < p_dimensions; j++) {
        C[i][j] = (p_statistics[p_dimensions*i+j])->Correlation();
      }
    }

    JAMA::Eigenvalue<double> E(C);
    TNT::Array2D<double> D, V;

    E.getD(D);
    E.getV(V);
    p_transform = TNT::Array2D<double>(V.dim1(), V.dim2());

    // The transform matrix needs to have the eigenvectors
    //  sorted in *descending* order
    //  So we need to reverse the order of V
    //   which is sorted in *ascending* order
    for(int i = 0; i < V.dim1(); i++) {
      for(int j = 0; j < V.dim2(); j++) {
        p_transform[i][j] = V[i][V.dim2()-j-1];
      }
    }

    ComputeInverse();

    p_hasTransform = true;
  }

  // Use LU decomposition to compute the inverse
  void PrincipalComponentAnalysis::ComputeInverse() {
    TNT::Array2D<double> id(p_transform.dim1(), p_transform.dim2(), 0.0);
    for(int i = 0; i < p_transform.dim1(); i++) id[i][i] = 1;

    JAMA::LU<double> lu(p_transform);
    if(lu.det() == 0.0) {
      std::string m = "Cannot take the inverse of the transform matrix";
      throw IException(IException::Programmer, m, _FILEINFO_);
    }

    p_inverse = lu.solve(id);
  }

  // Transform the vector into principal component space
  TNT::Array2D<double> PrincipalComponentAnalysis::Transform(TNT::Array2D<double> data) {
    if(data.dim1() != 1 || data.dim2() != p_dimensions) {
      QString m = "Transform input must be of dimension 1 x " +  QString::number(p_dimensions);
      throw IException(IException::Programmer, m, _FILEINFO_);
    }

    // the vector times the transform matrix
    return TNT::matmult(data, p_transform);
  }

  // Transform the vector from principal component space
  TNT::Array2D<double> PrincipalComponentAnalysis::Inverse(TNT::Array2D<double> data) {
    if(data.dim1() != 1 || data.dim2() != p_dimensions) {
      QString m = "Transform input must be of dimension 1 x " +  QString::number(p_dimensions);
      throw IException(IException::Programmer, m, _FILEINFO_);
    }

    // the vector times the inverse matrix
    return TNT::matmult(data, p_inverse);
  }
}