如何获得具有所有极端方差的 PCA 中所需的组件数量？

Question

我正在尝试获取分类所需的组件数量。我读过一个类似的问题 Finding the dimension with highest variance using scikit-learn PCA 和关于这个的 scikit 文档：

http://scikit-learn.org/dev/tutorial/statistical_inference/unsupervised_learning.html#principal-component-analysis-pca

但是，这仍然没有解决我的问题。我所有的 PCA 组件都非常大，因为我可以 select 所有这些组件，但如果我这样做，PCA 将毫无用处。

我也看了scikit learn中的PCA库 http://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html 表示L:

if n_components == ‘mle’, Minka’s MLE is used to guess the dimension if 0 < n_components < 1, select the number of components such that the amount of variance that needs to be explained is greater than the percentage specified by n_components

但是我找不到关于使用此技术分析 PCA n_components 的更多信息

下面是我的PCA分析代码：

from sklearn.decomposition import PCA
    pca = PCA()
    pca.fit(x_array_train)
    print(pca.explained_variance_)

结果：

   [  6.58902714e+50   6.23266555e+49   2.93568652e+49   2.25418736e+49
       1.10063872e+49   3.25107359e+40   4.72113817e+39   1.40411862e+39
       4.03270198e+38   1.60662882e+38   3.20028861e+28   2.35570241e+27
       1.54944915e+27   8.05181151e+24   1.42231553e+24   5.05155955e+23
       2.90909468e+23   2.60339206e+23   1.95672973e+23   1.22987336e+23
       9.67133111e+22   7.07208772e+22   4.49067983e+22   3.57882593e+22
       3.03546737e+22   2.38077950e+22   2.18424235e+22   1.79048845e+22
       1.50871735e+22   1.35571453e+22   1.26605081e+22   1.04851395e+22
       8.88191944e+21   6.91581346e+21   5.43786989e+21   5.05544020e+21
       4.33110823e+21   3.18309135e+21   3.06169368e+21   2.66513522e+21
       2.57173046e+21   2.36482212e+21   2.32203521e+21   2.06033130e+21
       1.89039408e+21   1.51882514e+21   1.29284842e+21   1.26103770e+21
       1.22012185e+21   1.07857244e+21   8.55143095e+20   4.82321416e+20
       2.98301261e+20   2.31336276e+20   1.31712446e+20   1.05253795e+20
       9.84992112e+19   8.27574150e+19   4.66007620e+19   4.09687463e+19
       2.89855823e+19   2.79035170e+19   1.57015298e+19   1.39218538e+19
       1.00594159e+19   7.31960049e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.29043685e+18   5.29043685e+18   5.29043685e+18
       5.29043685e+18   5.24952686e+18   2.09685699e+18   4.16588190e+17]

我尝试了 PCA(n_components = 'mle') 但是我遇到了这些错误..

    Traceback (most recent call last):
  File "xx", line 166, in <module>
    pca.fit(x_array_train)
  File "xx", line 225, in fit
    self._fit(X)
  File "/Users/lib/python2.7/site-packages/sklearn/decomposition/pca.py", line 294, in _fit
    n_samples, n_features)
  File "/Users/lib/python2.7/site-packages/sklearn/decomposition/pca.py", line 98, in _infer_dimension_
    ll[rank] = _assess_dimension_(spectrum, rank, n_samples, n_features)
  File "/Users/lib/python2.7/site-packages/sklearn/decomposition/pca.py", line 83, in _assess_dimension_
    (1. / spectrum_[j] - 1. / spectrum_[i])) + log(n_samples)
ValueError: math domain error

非常感谢您的帮助...

Answer 1

我没有使用 Python，但我在 C++ 和 opencv 中做了一些你需要的事情。希望你能成功将它转换成任何语言。

// choose how many eigenvectors you want:
int nEigensOfInterest = 0;
float sum = 0.0;
for (int i = 0; i < mEiVal.rows; ++i)
{
    sum += mEiVal.at<float>(i, 0);
    if (((sum * 100) / (sumOfEigens)) > 80)
    {
        nEigensOfInterest = i;
        break;
    }
}
logfile << "No of Eigens of interest: " << nEigensOfInterest << std::endl << std::endl;

基本思路是决定 "whatever %" 个需要继续进行的组件。我选择了 80。 mEiVal是特征值降序排列的列矩阵。 sumOfEigens 是所有特征值的总和。

我对scikit-learn没有经验，请告诉我，我会删除答案。

Answer 2

关于查找主成分分析中相关特征值数量的主题，有多项调查可用。我喜欢断棍法和平行分析。 Google 他们或看看 the tutorial of this lecture。

Answer 3

我只是自己学习这个，但在我看来，使用 0 < n_components < 1 的参考建议您可以将 n_components 设置为 0.85，以及组件的确切数量您需要解释将使用 85% 的方差。您还可以通过打印 sum(pca.explained_variance_) 来验证是否选择了正确数量的组件。您应该获得数据可能超过 0.85（或您选择的任何值）的最小方差百分比总和。

当然，还有更复杂的方法来选择多个组件，但根据经验，70% - 90% 是一个合理的开始。

Answer 4

我假设您的火车阵列 (x_array_train) 是这样标准化的：

from sklearn.preprocessing import StandardScaler
x_array_train = StandardScaler().fit_transform(x_array)

尽管如此，我的解决方案如下：

from sklearn.decomposition import PCA as pca
your_pca = pca(n_components = "mle", svd_solver ="full")
your_pca.fit_transform(x_array_train)
print(your_pca.explained_variance_)

通过这种方式，您应该获得尽可能少的主成分，因为 mle 算法允许您

如何获得具有所有极端方差的 PCA 中所需的组件数量？

How to get the number of components needed in PCA with all extreme variance?

pca

scikit-learn