principal.C: Principal Components Analysis (PCA) example

#include "TPrincipal.h"
#include "iomanip.h"
   
void principal(Int_t n=10, Int_t m=10000) 
{
  // 
  // Principal Components Analysis (PCA) example
  // 
  // Example of using TPrincipal as a stand alone class. 
  // 
  // We create n-dimensional data points, where c = trunc(n / 5) + 1
  // are  correlated with the rest n - c randomly distributed variables. 
  //
  // Here's the plot of the eigenvalues 

  //Authors: Rene Brun, Christian Holm Christensen
    
  Int_t c = n / 5 + 1;

  cout << "*************************************************" << endl; 
  cout << "*         Principal Component Analysis          *" << endl;
  cout << "*                                               *" << endl;
  cout << "*  Number of variables:           " << setw(4) << n 
       << "          *" << endl;
  cout << "*  Number of data points:         " << setw(8) << m
       << "      *" << endl;
  cout << "*  Number of dependent variables: " << setw(4) << c
       << "          *" << endl;
  cout << "*                                               *" << endl;
  cout << "*************************************************" << endl; 
  
      
  // Initilase the TPrincipal object. Use the empty string for the
  // final argument, if you don't wan't the covariance
  // matrix. Normalising the covariance matrix is a good idea if your
  // variables have different orders of magnitude. 
  TPrincipal* principal = new TPrincipal(n,"ND");
  
  // Use a pseudo-random number generator
  TRandom* random = new TRandom;
  
  // Make the m data-points
  // Make a variable to hold our data
  // Allocate memory for the data point
  Double_t* data = new Double_t[n];
  for (Int_t i = 0; i < m; i++) {

    // First we create the un-correlated, random variables, according
    // to one of three distributions 
    for (Int_t j = 0; j < n - c; j++) {
      if (j % 3 == 0)
	data[j] = random->Gaus(5,1);
      else if (j % 3 == 1)
	data[j] = random->Poisson(8);
      else 
	data[j] = random->Exp(2);
    }

    // Then we create the correlated variables
    for (Int_t j = 0 ; j < c; j++) {
      data[n - c + j] = 0;
      for (Int_t k = 0; k < n - c - j; k++)
	data[n - c + j] += data[k];
    }
    
    // Finally we're ready to add this datapoint to the PCA
    principal->AddRow(data);
  }
    
  // We delete the data after use, since TPrincipal got it by now. 
  delete [] data;
  
  // Do the actual analysis
  principal->MakePrincipals();
  
  // Print out the result on
  principal->Print();

  // Test the PCA 
  principal->Test();

  // Make some histograms of the orginal, principal, residue, etc data 
  principal->MakeHistograms();
  
  // Make two functions to map between feature and pattern space 
  principal->MakeCode();

  // Start a browser, so that we may browse the histograms generated
  // above 
  TBrowser* b = new TBrowser("principalBrowser", principal);
  
}