PCA python

pca

# -*- coding: utf-8 -*-
from numpy import mean,cov,double,cumsum,dot,linalg,array,rank
from pylab import plot,subplot,axis,stem,show,figure

def princomp(A):
 """ performs principal components analysis 
     (PCA) on the n-by-p data matrix A
     Rows of A correspond to observations, columns to variables. 

 Returns :  
  coeff :
    is a p-by-p matrix, each column containing coefficients 
    for one principal component.
  score : 
    the principal component scores; that is, the representation 
    of A in the principal component space. Rows of SCORE 
    correspond to observations, columns to components.
  latent : 
    a vector containing the eigenvalues 
    of the covariance matrix of A.
 """
 # computing eigenvalues and eigenvectors of covariance matrix
 M = (A-mean(A.T,axis=1)).T # subtract the mean (along columns)
 [latent,coeff] = linalg.eig(cov(M)) # attention:not always sorted
 score = dot(coeff.T,M) # projection of the data in the new space
 return coeff,score,latent
 
A = array([ [2.4,0.7,2.9,2.2,3.0,2.7,1.6,1.1,1.6,0.9],
            [2.5,0.5,2.2,1.9,3.1,2.3,  2,  1,1.5,1.1] ])

coeff, score, latent = princomp(A.T)

figure()
subplot(121)
# every eigenvector describe the direction
# of a principal component.
m = mean(A,axis=1)
plot([0, -coeff[0,0]*2]+m[0], [0, -coeff[0,1]*2]+m[1],'--k')
plot([0, coeff[1,0]*2]+m[0], [0, coeff[1,1]*2]+m[1],'--k')
plot(A[0,:],A[1,:],'ob') # the data
axis('equal')
subplot(122)
# new data
plot(score[0,:],score[1,:],'*g')
axis('equal')
show()