In sklearn an numpy there are different ways to compute the first principal component. I obtain a different results for each method. Why?
import matplotlib.pyplot as pl
from sklearn import decomposition
import scipy as sp
import sklearn.preprocessing
import numpy as np
import sklearn as sk
def gen_data_3_1():
#### generate the data 3.1
m=1000 # number of samples
n=10 # number of variables
d1=np.random.normal(loc=0,scale=100,size=(m,1))
d2=np.random.normal(loc=0,scale=121,size=(m,1))
d3=-0.2*d1+0.9*d2
z=np.zeros(shape=(m,1))
for i in range(4):
z=np.hstack([z,d1+np.random.normal(size=(m,1))])
for i in range(4):
z=np.hstack([z,d2+np.random.normal(size=(m,1))])
for i in range(2):
z=np.hstack([z,d3+np.random.normal(size=(m,1))])
z=z[:,1:11]
z=sk.preprocessing.scale(z,axis=0)
return z
x=gen_data_3_1() #generate the sample dataset
x=sk.preprocessing.scale(x) #normalize the data
pca=sk.decomposition.PCA().fit(x) #compute the PCA of x and print the first princ comp.
print "first pca components=",pca.components_[:,0]
u,s,v=sp.sparse.linalg.svds(x) # the first column of v.T is the first princ comp
print "first svd components=",v.T[:,0]
trsvd=sk.decomposition.TruncatedSVD(n_components=3).fit(x) #the first components is the
#first princ comp
print "first component TruncatedSVD=",trsvd.components_[0,]
--
first pca components= [-0.04201262 0.49555992 0.53885401 -0.67007959 0.0217131 -0.02535204
0.03105254 -0.07313795 -0.07640555 -0.00442718]
first svd components= [ 0.02535204 -0.1317925 0.12071112 -0.0323422 0.20165568 -0.25104996
-0.0278177 0.17856688 -0.69344318 0.59089451]
first component TruncatedSVD= [-0.04201262 -0.04230353 -0.04213402 -0.04221069 0.4058159 0.40584108
0.40581564 0.40584842 0.40872029 0.40870925]
