主成分分析:变换后各成分的顺序

Question

我使用sklearn.decomposition中的PCA类来降低特征空间的维数，以便绘制该特征空间。

我想知道以下内容:在应用PCA类的fit和transform方法后，我得到了文档中所述形状为(n_samples, n_components)的数组X_transformed。X_transformed列的顺序是否按解释方差的数量排序?在文档中，它说PCA.components_是按解释方差排序的，所以我假设X_transformed的列也是如此，但如果我错了，请纠正我。

小例子:

from sklearn.decomposition import PCA

pca = PCA()
pca.fit(X) # X is an array containing my original features. X.shape=(n_samples, n_features)
X_transformed = pca.transfom(X) # X_transformed.shape=(n_samples, n_components). Are X_transformed's columns sorted by explained variance?

谢谢!

Answer 1

嗯，也许我只是想测试一下

from sklearn.decomposition import PCA
import numpy as np

pca_2 = PCA(n_components=2)
X_transformed_2 = pca_2.fit_transform(X)
# X_transformed_2 hold two components with most variance explained
pca_10 = PCA(n_components=10)
X_transformed_10 = pca_10.fit_transform(X)
# X_transformed_10 hold 10 components with most variance explained

# Hypothesis: If the first 2 components in X_transformed_10 are ordered by explained variance, it's first 2 columns should equal X_transformed_2
np.array_equal(X_transformed_2, X_transformed_10[:, 2]) ## returns True