Python3.x 在 sklearn.decomposition.PCA 中，为什么 components_ 是负数

我正试图跟随Abdi&amp；Williams-Principal Component Analysis(2010)，并使用numpy.linalg.svd通过SVD构建主要组件.

当我用sklearn显示拟合PCA的components_属性时，它们的大小与我手动计算的完全相同，但some(不是全部)的符号相反.这是什么原因？

Update:我下面的(部分)答案包含一些额外的信息.

以以下数据为例:

from pandas_datareader.data import DataReader as dr
import numpy as np
from sklearn.decomposition import PCA
from sklearn.preprocessing import scale

# sample data - shape (20, 3), each column standardized to N~(0,1)
rates = scale(dr(['DGS5', 'DGS10', 'DGS30'], 'fred', 
           start='2017-01-01', end='2017-02-01').pct_change().dropna())

# with sklearn PCA:
pca = PCA().fit(rates)
print(pca.components_)
[[-0.58365629 -0.58614003 -0.56194768]
 [-0.43328092 -0.36048659  0.82602486]
 [-0.68674084  0.72559581 -0.04356302]]

# compare to the manual method via SVD:
u, s, Vh = np.linalg.svd(np.asmatrix(rates), full_matrices=False)
print(Vh)
[[ 0.58365629  0.58614003  0.56194768]
 [ 0.43328092  0.36048659 -0.82602486]
 [-0.68674084  0.72559581 -0.04356302]]

# odd: some, but not all signs reversed
print(np.isclose(Vh, -1 * pca.components_))
[[ True  True  True]
 [ True  True  True]
 [False False False]]