Consider the following pieces of code and their associated outputs.
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import load_iris
iris = load_iris()
X = iris.data
y = iris.target
data = X
n_components = data.shape[1]
scaler = StandardScaler().fit(data)
data = scaler.transform(data)
pca = PCA(n_components=n_components, random_state=4)
pca = pca.fit(data)
pca.singular_values_
pca.components_
array([20.92306556, 11.7091661 , 4.69185798, 1.76273239])
array([[ 0.52106591, -0.26934744, 0.5804131 , 0.56485654],
[ 0.37741762, 0.92329566, 0.02449161, 0.06694199],
[-0.71956635, 0.24438178, 0.14212637, 0.63427274],
[-0.26128628, 0.12350962, 0.80144925, -0.52359713]])
for row in pca.components_:
print(np.linalg.norm(row, ord=2))
0.9999999999999997
0.9999999999999994
1.0
1.0
I noticed that the length (=euclidean norm) of all my principal components is 1. Why is that? I thought that the principal components are the eigenvectors of the covariance matrix and do not necessarily have unit length.
Update: Added the singular values. They are indeed all different. However, when applying PCA in order to transform data, they are not used. See relevant code here: https://github.com/scikit-learn/scikit-learn/blob/dfc5e16066b3a3bbf34238cc0f67639d0965f1a8/sklearn/decomposition/_base.py#L129 Only self.components_ are used, which all have length one.
