python - Sklearn PCA 解释方差和解释方差比差异

Question

我正在尝试从特征向量中获取方差。
explained_variance_ratio_有什么区别和 explained_variance_在 PCA ?

Answer 1

解释方差的 百分比 是:

explained_variance_ratio_

方差 即协方差矩阵的特征值是:

explained_variance_

公式: explained_variance_ratio_ = explained_variance_ / np.sum(explained_variance_)
示例:

import numpy as np
from sklearn.decomposition import PCA
X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
pca = PCA(n_components=2)
pca.fit(X)  

pca.explained_variance_
array([7.93954312, 0.06045688]) # the actual eigenvalues (variance)

pca.explained_variance_ratio_ # the percentage of the variance
array([0.99244289, 0.00755711])

同样基于上述公式:
7.93954312 / (7.93954312+ 0.06045688) = 0.99244289
从文档:

explained_variance_ : array, shape (n_components,) The amount of variance explained by each of the selected components.

Equal to n_components largest eigenvalues of the covariance matrix of X.

New in version 0.18.

explained_variance_ratio_ : array, shape (n_components,) Percentage of variance explained by each of the selected components.

If n_components is not set then all components are stored and the sum of the ratios is equal to 1.0.