为什么 sklearn 的 PCA 不是 return 可重现的结果？

Question

我正在使用 scikit's PCA 并注意到一些非常奇怪的行为。本质上，当使用超过 500 个样本时，结果是不可重现的。这个例子展示了正在发生的事情：

import numpy as np
from sklearn.decomposition import PCA

Ncomp = 15
Nsamp = 501
Nfeat = 30

PCAnalyzer = PCA(n_components = Ncomp)
ManySamples = np.random.rand(Nsamp, Nfeat)
TestSample = np.ones((1, Nfeat))

print(PCAnalyzer.fit(ManySamples).transform(TestSample))
print(PCAnalyzer.fit(ManySamples).transform(TestSample))
print(PCAnalyzer.fit(ManySamples).transform(TestSample))
print(PCAnalyzer.fit(ManySamples).transform(TestSample))

它输出：

>>> print(PCAnalyzer.fit(ManySamples).transform(TestSample))
[[-0.25641111  0.42327221  0.4616427  -0.72047479 -0.12386481  0.10608497
   0.28739712 -0.26003239  1.27305465  1.05307604 -0.53915119 -0.07127874
   0.25312454 -0.12052255 -0.06738885]]
>>> print(PCAnalyzer.fit(ManySamples).transform(TestSample))
[[-0.26656397  0.42293446  0.45487161 -0.7339531  -0.16134778  0.15389179
   0.27052166 -0.33565591  1.26289845  0.96118269  0.5362569  -0.54688338
   0.08329318 -0.08423136 -0.00253318]]
>>> print(PCAnalyzer.fit(ManySamples).transform(TestSample))
[[-0.21899525  0.38527988  0.45101669 -0.73443888 -0.20501978  0.09640448
   0.17826649 -0.37653009  1.04856884  1.10948052  0.60700417 -0.39864793
   0.18020651  0.08061955  0.05383696]]
>>> print(PCAnalyzer.fit(ManySamples).transform(TestSample))
[[-0.27070256  0.41532602  0.45936926 -0.73820121 -0.18160026 -0.13139435
   0.28015907 -0.28144421  1.16554587  1.00472104  0.16983399 -0.67157762
  -0.3005816   0.54645421  0.09807374]]

将样本数 (Nsamp) 减少到 500 或更少，或将组件数 (Ncomp) 增加到 20 或更多，可以解决问题 - 但这对我.

Answer 1

有时，阅读文档会有所帮助：

It uses the LAPACK implementation of the full SVD or a randomized truncated SVD by the method of Halko et al. 2009, depending on the shape of the input data and the number of components to extract.

这解决了问题：

PCAnalyzer = PCA(n_components = Ncomp, svd_solver = 'full')

Answer 2

这是因为 sklearn 使用的默认求解器。来自 docs:

the solver is selected by a default policy based on X.shape and n_components: if the input data is larger than 500x500 and the number of components to extract is lower than 80% of the smallest dimension of the data, then the more efficient ‘randomized’ method is enabled. Otherwise the exact full SVD is computed and optionally truncated afterwards.

如果您需要可重现的结果，请使用不同的求解器，或设置 random_state

为什么 sklearn 的 PCA 不是 return 可重现的结果？

Why does sklearn's PCA not return reproducible results?

python

pca

scikit-learn