Canonical Correlation Analysis in Python with sklearn

Question

I'm trying to use sklearn to carry out Canonical Correlation Analysis (CCA). I'm starting with the simple example that is included in the manual:

from sklearn.cross_decomposition import CCA
X = [[0., 0., 1.], [1.,0.,0.], [2.,2.,2.], [3.,5.,4.]]
Y = [[0.1, -0.2], [0.9, 1.1], [6.2, 5.9], [11.9, 12.3]]
cca = CCA(n_components=1)
cca.fit(X, Y)

X_c, Y_c = cca.transform(X, Y)

I understand that in cca.x_weights_ I get the "canonical coefficents", i.e., the linear combinations of the original X variables (the columns of matrices "A" and "B" returned by MATLAB). However, where are the the "canonical correlations", i.e, the maximum correlation reached when applying the transformation given by the canonical coeficients (i.e., vector "r" returned by MATLAB). Is it possible to also get that in Python?

Answer 1

You can calculate the correlations using the outputs of .transfrom. This can be done with either numpy or scipy. I prefer scipy's stats module:

X_c, Y_c = cca.transform(X, Y)
import scipy.stats
corrcoef,p_value = scipy.stats.pearsonr(X_c,Y_c)

Clearly, since in your case you don't have enough samples (i.e., n < p+q), you're correlation is 1.