Python Implementation Of Canonical Correlation
- first import NumPy as np. We then define two arrays, X and Y, representing two sets of variables.
- Next, we center the data by subtracting the mean of each variable from the respective variables in X and Y.
- We calculate the covariance matrix between the centered X and Y using np.cov(X_centered.T, Y_centered.T).
- Then, we perform singular value decomposition (SVD) on the covariance matrix to obtain matrices
- Finally, we calculate the canonical correlation coefficients as the square root of the singular values (s) obtained from SVD.
import numpy as np
X = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])
Y = np.array([[-1, -2], [-3, -4], [-5, -6], [-7, -8]])
# Mean centering
X_centered = X - X.mean(axis=0)
Y_centered = Y - Y.mean(axis=0)
# Calculate covariance matrix
covariance_matrix = np.cov(X_centered.T, Y_centered.T)
# Singular value decomposition
U, s, Vt = np.linalg.svd(covariance_matrix)
# Calculate canonical correlation coefficient
canonical_corr = np.sqrt(s)
print("Canonical Correlation Coefficients:", canonical_corr)
Output:
Canonical Correlation Coefficients: [7.63762616e+00 5.16704216e-08 3.46215750e-08 0.00000000e+00 0.00000000e+00]
Thus, CCA is a powerful multivariate statistical technique that can help you explore the relationships between two sets of variables. While it has its limitations, it can provide valuable insights into the structure of your data. By understanding the principles and procedures of CCA, you can effectively use this technique in your research.
What is Canonical Correlation Analysis?
Canonical Correlation Analysis (CCA) is an advanced statistical technique used to probe the relationships between two sets of multivariate variables on the same subjects. It is particularly applicable in circumstances where multiple regression would be appropriate, but there are multiple intercorrelated outcome variables. CCA identifies and quantifies the associations among these two variable groups. It computes a set of canonical variates, which are orthogonal linear combinations of the variables within each group, that optimally explain the variability both within and between the groups.