Sklearn PCA not working
I am playing with sclearn PCA and it is behaving strangely.
from sklearn.decomposition import PCA
import numpy as np
identity = np.identity(10)
pca = PCA(n_components=10)
augmented_identity = pca.fit_transform(identity)
np.linalg.norm(identity - augmented_identity)
4.5997749080745738
Note that I am setting the number of measurements to 10. Shouldn't the rate be 0?
Any insight as to why this is not the case would be appreciated.
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1 answer
Although the PCA calculates the orthogonal components based on the covariance matrix, the input to the PCA in sklearn is a data matrix instead of a covariance / correlation matrix.
import numpy as np
from sklearn.decomposition import PCA
# gaussian random variable, 10-dimension, identity cov mat
X = np.random.randn(100000, 10)
pca = PCA(n_components=10)
X_transformed = pca.fit_transform(X)
np.linalg.norm(np.cov(X.T) - np.cov(X_transformed.T))
Out[219]: 0.044691263454134933
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