machine learning - Fast ICA using scikit learn- reconstruction error analysis -


i trying use fastica procedure in scikitlearn. validation purposes tried understand difference between pca , ica based signal reconstruction.

the original number of observed signals 6 , tried use 3 reconstruction independent components . problem both ica , pca result in same reconstruction errors no matter norm use. can 1 throw light happening here.

the code below:

 pca = pca(n_components=3)  icamodel = fastica(n_components=3,whiten=true)   data = trainingdatadict[yearspan][riskfactornames]   pcr_dict[yearspan] = pd.dataframe(pca.fit_transform(data),                                     columns=['pc1','pc2','pc3'],index=data.index)   icr_dict[yearspan] = pd.dataframe(icamodel.fit_transform(data),                                     columns=['ic1','ic2','ic3'],index=data.index)  '------------------------inverse transform of ic , pcs -----------'   pca_new_data_df = pd.dataframe(pca.inverse_transform(pcr_dict[yearspan]),                                    columns =['f1','f2','f3'],index = data.index)   ica_new_data_df = pd.dataframe(icamodel.inverse_transform(icr_dict[yearspan]),                                    columns =['f1','f2','f3'],index = data.index)

below way measure reconstruction error

'-----------reconstruction errors------------------'  print 'pca reconstruction error l2 norm:',np.sqrt((pca_new_data_df - data).apply(np.square).mean())   print 'ica reconstruction error l2 norm:',np.sqrt((ica_new_data_df - data).apply(np.square).mean())   print 'pca reconstruction error l1 norm:',(pca_new_data_df - data).apply(np.absolute).mean()   print 'ica reconstruction error l1 norm:',(ica_new_data_df - data).apply(np.absolute).mean()

below description of tails of pc , ics

pc stats :  ('2003', '2005')         kurtosis  skewness pcr_1 -0.001075 -0.101006 pcr_2  1.057140  0.316163 pcr_3  1.067471  0.047946   ic stats :  ('2003', '2005')         kurtosis  skewness icr_1 -0.221336 -0.204362 icr_2  1.499278  0.433495 icr_3  3.654237  0.072480

below results of reconstruction

pca reconstruction error l2 norm:  sptr        0.000601 sptrmdcp    0.001503 ru20intr    0.000788 lbustruu    0.002311 lf98truu    0.001811 nddueafe    0.000135 dtype: float64   ica reconstruction error l2 norm :  sptr        0.000601 sptrmdcp    0.001503 ru20intr    0.000788 lbustruu    0.002311 lf98truu    0.001811 nddueafe    0.000135

even l1 norms same. bit confused!


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