通过 sklearn.decomposition.PCA 执行 svd ，我怎样才能从中得到 U S V？

Question

我用 sklearn.decomposition.PCA

执行 SVD

来自SVD的方程

A= U x S x V_t

V_t = V 的转置矩阵（对不起，我不能粘贴原来的等式）

如果我想要U、S、V矩阵，用sklearn.decomposition.PCA怎么得到？

Answer 1

首先，根据矩阵的大小，PCA 的 sklearn 实现并不总是计算完整的 SVD 分解。以下摘自PCA's GitHub reciprocity:

svd_solver : string {'auto', 'full', 'arpack', 'randomized'}
        auto :
            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.
        full :
            run exact full SVD calling the standard LAPACK solver via
            `scipy.linalg.svd` and select the components by postprocessing
        arpack :
            run SVD truncated to n_components calling ARPACK solver via
            `scipy.sparse.linalg.svds`. It requires strictly
            0 < n_components < X.shape[1]
        randomized :
            run randomized SVD by the method of Halko et al.

此外，它还对数据执行一些操作（参见 here）。

现在，如果您想获得 sklearn.decomposition.PCA 中使用的 U, S, V，您可以使用 pca._fit(X)。例如：

from sklearn.decomposition import PCA
X = np.array([[1, 2], [3,5], [8,10], [-1, 1], [5,6]])
pca = PCA(n_components=2)
pca._fit(X)

打印

(array([[ -3.55731195e-01,   5.05615563e-01],
        [  2.88830295e-04,  -3.68261259e-01],
        [  7.10884729e-01,  -2.74708608e-01],
        [ -5.68187889e-01,  -4.43103380e-01],
        [  2.12745524e-01,   5.80457684e-01]]),
 array([ 9.950385  ,  0.76800941]),
 array([[ 0.69988535,  0.71425521],
        [ 0.71425521, -0.69988535]]))

但是，如果你只想对原始数据进行SVD分解，我建议使用scipy.linalg.svd

通过 sklearn.decomposition.PCA 执行 svd ，我怎样才能从中得到 U S V？

Performing svd by sklearn.decomposition.PCA , how can I get the U S V from this?

python

pca

svd