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wangz10/pca_svd_relationship_np.py

Created March 16, 2019 14:34
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pca_svd_relationship_np.py
# Compute covariance matrix
C = np.dot(X.T, X) / (n-1)
# Eigen decomposition
eigen_vals, eigen_vecs = np.linalg.eig(C)
# SVD
U, Sigma, Vh = np.linalg.svd(X,
full_matrices=False,
compute_uv=True)
# Relationship between singular values and eigen values:
print(np.allclose(np.square(Sigma) / (n - 1), eigen_vals)) # True
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wangz10 commented May 23, 2020

@nvishnya X need to be z-score transformed: subtract mean then divided by standard deviation.

Actually it only need to be centered around 0 for them to be equivalent:

X = X - X.mean(axis=0)

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