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

Question

I perform SVD with sklearn.decomposition.PCA

From the equation of the SVD

A= U x S x V_t

V_t = transpose matrix of V (Sorry I can't paste the original equation)

If I want the matrix U, S, and V, how can I get it if I use the sklearn.decomposition.PCA ?

Answer 1

First of all, depending on the size of your matrix, sklearn implementation of PCA will not always compute the full SVD decomposition. The following is taken from 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.

In addition, it also performs some manipulations on the data (see here).

Now, if you want to get U, S, V that are used in sklearn.decomposition.PCA you can use pca._fit(X). For example:

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)

prints

(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]]))

However, if you just want the SVD decomposition of the original data, I would suggest to use scipy.linalg.svd