Cannot manually reproduce CCA loadings For my current project I am using sklearn.cross_decomposition.CCA. On several wepages (e.g. https://stats.idre.ucla.edu/r/dae/canonical-correlation-analysis/ or https://www.uaq.mx/statsoft/stcanan.html or https://pure.uvt.nl/ws/portalfiles/portal/596531/useofcaa_ab5.pdf) it says that canonical loadings can be computed as correlations between variables and the canonical variates. However, I could not reproduce this using scipy.stats.pearsonr? Is this just false information or am I doing something wrong?
Here's an example
from sklearn.cross_decomposition import CCA
import numpy as np
from scipy.stats import pearsonr

# compute CCA
X = np.array([[0., 0., 1.], [1.,0.,0.], [2.,2.,2.], [3.,5.,4.]])
Y = np.array([[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)

# obtain loadings for X variable set
x_loadings = cca.x_loadings_

print(f"The first variable has a loading of {x_loadings[0]} on the first canonical variate")

# try to manually calculate loadings using pearson correlation. 
r,_ = pearsonr(np.squeeze(X[:,0]),np.squeeze(X_c))

print(f"Correlation between first variable and first canonical variate: {r}")


which gives you:
The first variable has a loading of [0.61454275] on the first canonical variate
Correlation between first variable and first canonical variate: 0.9610851804703184

As you can see those numbers are totally different...

I found the solution. Indeed user rep_ho was right, I did something wrong by not standardizing the X matrix before doing the calculations.   Doing the following before calculating the correlation solved the problem:
from scipy.stats import zscore
X = zscore(X,ddof=1)

Additional notes (not relevant for this thread):
Further referring to the first point of rep_ho's answer, X_c can be reproduced by multiplying the standardized feature matrix with cca.x_weights:
X_c = np.matmul(X,x_weights)

That means that cca.x_weights is what rep_ho is referring to as "variable weights or parameters".
