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principal.py File Reference

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Principal Components Analysis (PCA) example

Example of using TPrincipal as a stand alone class.

I create n-dimensional data points, where c = trunc(n / 5) + 1 are correlated with the rest n - c randomly distributed variables.

Based on principal.C by Rene Brun and Christian Holm Christensen

Variable # | Mean Value | Sigma | Eigenvalue
-------------+------------+------------+------------
0 | 4.994 | 0.9926 | 0.3856
1 | 8.011 | 2.824 | 0.112
2 | 2.017 | 1.992 | 0.1031
3 | 4.998 | 0.9952 | 0.1022
4 | 8.019 | 2.794 | 0.09998
5 | 1.976 | 2.009 | 0.0992
6 | 4.996 | 0.9996 | 0.09794
7 | 35.01 | 5.147 | 1.409e-16
8 | 30.01 | 5.041 | 2.723e-16
9 | 28.04 | 4.644 | 4.578e-16
Writing on file "pca.C" ... done
*************************************************
* Principal Component Analysis *
* *
* Number of variables: 10 *
* Number of data points: 10000 *
* Number of dependent variables: 3 *
* *
*************************************************
from ROOT import TPrincipal, gRandom, TBrowser, vector
n = 10
m = 10000
c = int(n / 5) + 1
print ("""*************************************************
* Principal Component Analysis *
* *
* Number of variables: {0:4d} *
* Number of data points: {1:8d} *
* Number of dependent variables: {2:4d} *
* *
*************************************************""".format(n, m, c))
# 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.
principal = TPrincipal(n, "ND")
# Use a pseudo-random number generator
randumNum = gRandom
# Make the m data-points
# Make a variable to hold our data
# Allocate memory for the data point
data = vector('double')()
for i in range(m):
# First we create the un-correlated, random variables, according
# to one of three distributions
for j in range(n - c):
if j % 3 == 0:
data.push_back(randumNum.Gaus(5, 1))
elif j % 3 == 1:
data.push_back(randumNum.Poisson(8))
else:
data.push_back(randumNum.Exp(2))
# Then we create the correlated variables
for j in range(c):
data.push_back(0)
for k in range(n - c - j):
data[n - c + j] += data[k]
# Finally we're ready to add this datapoint to the PCA
principal.AddRow(data.data())
data.clear()
# 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
# Start a browser, so that we may browse the histograms generated
# above
principal.MakeCode()
b = TBrowser("principalBrowser", principal)
Using a TBrowser one can browse all ROOT objects.
Definition: TBrowser.h:37
Authors
Juan Fernando, Jaramillo Botero

Definition in file principal.py.