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principal.C
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1/// \file
2/// \ingroup tutorial_math
3/// \notebook
4/// Principal Components Analysis (PCA) example
5///
6/// Example of using TPrincipal as a stand alone class.
7///
8/// We create n-dimensional data points, where c = trunc(n / 5) + 1
9/// are correlated with the rest n - c randomly distributed variables.
10///
11/// \macro_output
12/// \macro_code
13///
14/// \authors Rene Brun, Christian Holm Christensen
15
16#include "TPrincipal.h"
17
18void principal(Int_t n=10, Int_t m=10000)
19{
20 Int_t c = n / 5 + 1;
21
22 cout << "*************************************************" << endl;
23 cout << "* Principal Component Analysis *" << endl;
24 cout << "* *" << endl;
25 cout << "* Number of variables: " << setw(4) << n
26 << " *" << endl;
27 cout << "* Number of data points: " << setw(8) << m
28 << " *" << endl;
29 cout << "* Number of dependent variables: " << setw(4) << c
30 << " *" << endl;
31 cout << "* *" << endl;
32 cout << "*************************************************" << endl;
33
34
35 // Initilase the TPrincipal object. Use the empty string for the
36 // final argument, if you don't wan't the covariance
37 // matrix. Normalising the covariance matrix is a good idea if your
38 // variables have different orders of magnitude.
39 TPrincipal* principal = new TPrincipal(n,"ND");
40
41 // Use a pseudo-random number generator
42 TRandom* randumNum = new TRandom;
43
44 // Make the m data-points
45 // Make a variable to hold our data
46 // Allocate memory for the data point
47 Double_t* data = new Double_t[n];
48 for (Int_t i = 0; i < m; i++) {
49
50 // First we create the un-correlated, random variables, according
51 // to one of three distributions
52 for (Int_t j = 0; j < n - c; j++) {
53 if (j % 3 == 0) data[j] = randumNum->Gaus(5,1);
54 else if (j % 3 == 1) data[j] = randumNum->Poisson(8);
55 else data[j] = randumNum->Exp(2);
56 }
57
58 // Then we create the correlated variables
59 for (Int_t j = 0 ; j < c; j++) {
60 data[n - c + j] = 0;
61 for (Int_t k = 0; k < n - c - j; k++) data[n - c + j] += data[k];
62 }
63
64 // Finally we're ready to add this datapoint to the PCA
66 }
67
68 // We delete the data after use, since TPrincipal got it by now.
69 delete [] data;
70
71 // Do the actual analysis
72 principal->MakePrincipals();
73
74 // Print out the result on
75 principal->Print();
76
77 // Test the PCA
78 principal->Test();
79
80 // Make some histograms of the orginal, principal, residue, etc data
81 principal->MakeHistograms();
82
83 // Make two functions to map between feature and pattern space
84 principal->MakeCode();
85
86 // Start a browser, so that we may browse the histograms generated
87 // above
88 TBrowser* b = new TBrowser("principalBrowser", principal);
89}
#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
Option_t Option_t TPoint TPoint const char GetTextMagnitude GetFillStyle GetLineColor GetLineWidth GetMarkerStyle GetTextAlign GetTextColor GetTextSize void data
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
TMarker m
Definition textangle.C:8