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principal.C File Reference

## Detailed Description

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.

*************************************************
* Principal Component Analysis *
* *
* Number of variables: 10 *
* Number of data points: 10000 *
* Number of dependent variables: 3 *
* *
*************************************************
Variable # | Mean Value | Sigma | Eigenvalue
-------------+------------+------------+------------
0 | 5.008 | 1.005 | 0.3851
1 | 7.998 | 2.861 | 0.1107
2 | 1.967 | 1.956 | 0.1036
3 | 5.016 | 1.005 | 0.1015
4 | 8.009 | 2.839 | 0.1008
5 | 2.013 | 1.973 | 0.09962
6 | 4.992 | 1.014 | 0.09864
7 | 35 | 5.156 | 6.481e-16
8 | 30.01 | 5.049 | 2.202e-16
9 | 28 | 4.649 | 5.497e-16
Writing on file "pca.C" ... done
#include "TPrincipal.h"
void principal(Int_t n=10, Int_t m=10000)
{
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.
// Use a pseudo-random number generator
TRandom* randumNum = 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] = randumNum->Gaus(5,1);
else if (j % 3 == 1) data[j] = randumNum->Poisson(8);
else data[j] = randumNum->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];
}
}
// 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);
}
#define b(i)
Definition RSha256.hxx:100
#define c(i)
Definition RSha256.hxx:101
int Int_t
Definition RtypesCore.h:45
double Double_t
Definition RtypesCore.h:59
Using a TBrowser one can browse all ROOT objects.
Definition TBrowser.h:37
Principal Components Analysis (PCA)
Definition TPrincipal.h:21
This is the base class for the ROOT Random number generators.
Definition TRandom.h:27
virtual Double_t Gaus(Double_t mean=0, Double_t sigma=1)
Samples a random number from the standard Normal (Gaussian) Distribution with the given mean and sigm...
Definition TRandom.cxx:274
virtual Int_t Poisson(Double_t mean)
Generates a random integer N according to a Poisson law.
Definition TRandom.cxx:402
virtual Double_t Exp(Double_t tau)
Returns an exponential deviate.
Definition TRandom.cxx:251
const Int_t n
Definition legend1.C:16
auto * m
Definition textangle.C:8

Definition in file principal.C.