scipy - TruncatedSVD 和 svds 的区别

Question

我看到sklearn.decomposition.TruncatedSVD和scipy.sparse.linalg.svds的文档都提到它们都SVD适用于稀疏矩阵。它们之间有什么区别？

谢谢。

Answer 1

TruncatedSVD功能更丰富。它具有scikit-learn API，因此您可以将其放入sklearn.Pipeline对象中并调用transform新矩阵，而不必自己计算矩阵乘法。它提供了两种算法：快速随机 SVD 求解器（默认），或scipy.sparse.svds.

（完全披露：我写TruncatedSVD的。）

Answer 2

有同样的做法

#check how to use TRuncatedSVD
X=[[1,2,3],[1,4,2],[4,1,7],[5,6,8]]

# TRUNCATED SVD
from sklearn.decomposition import TruncatedSVD
svd = TruncatedSVD(n_components=2, n_iter=7, random_state=42)

US=svd.fit_transform(X)

V=svd.components_
S=svd.singular_values_ 
print('u,s,v', US,S,V)
print('X_restored dot way',np.round(np.dot(US,V),1),'svdinverse way',np.round(svd.inverse_transform(U),1))

# LINALG SVD

U1,S1,V1=np.linalg.svd(X)

print('u1,s1,v1 remark negative mirrored',U1[:,:2]*S1[:2],V1[:2,:])
print('X restored u1,s1,v1, 2 components',np.round( np.dot( U1[:,:2]*S1[:2],V1[:2,:] ),1 ) ) 

# sparse svd
from scipy.sparse import csc_matrix
from scipy.sparse.linalg import svds, eigs
A = csc_matrix(X, dtype=float)

u2, s2, vt2 = svds(A, k=2)

print('sparse reverses !',u2*s2,vt2)
print('x restored',np.round( np.dot(u2*s2,vt2),1) )

结果

    u,s,v [[ 3.66997034 -0.34754761]
 [ 3.82764223 -2.51681397]
 [ 7.61154768  2.83860088]
 [11.13470337 -0.96070751]] [14.49264657  3.92883644] [[ 0.44571865  0.46215842  0.76664495]
 [ 0.23882889 -0.88677195  0.39572247]]
X_restored dot way
 [[1.6 2.  2.7]
 [1.1 4.  1.9]
 [4.1 1.  7. ]
 [4.7 6.  8.2]]
svdinverse way
 [[1.6 2.  2.7]
 [1.1 4.  1.9]
 [4.1 1.  7. ]
 [4.7 6.  8.2]]
u1,s1,v1 remark negative mirrored
 [[ -3.66997034   0.34754761]
 [ -3.82764223   2.51681397]
 [ -7.61154768  -2.83860088]
 [-11.13470337   0.96070751]] [[-0.44571865 -0.46215842 -0.76664495]
 [-0.23882889  0.88677195 -0.39572247]]
X restored u1,s1,v1, 2 components
 [[1.6 2.  2.7]
 [1.1 4.  1.9]
 [4.1 1.  7. ]
 [4.7 6.  8.2]]
sparse reverses !
 [[-0.34754761  3.66997034]
 [-2.51681397  3.82764223]
 [ 2.83860088  7.61154768]
 [-0.96070751 11.13470337]]
 [[ 0.23882889 -0.88677195  0.39572247]
 [ 0.44571865  0.46215842  0.76664495]]
x restored
 [[1.6 2.  2.7]
 [1.1 4.  1.9]
 [4.1 1.  7. ]
 [4.7 6.  8.2]]
[[-0.25322982  0.0884607   0.88223679]
 [-0.26410926  0.64060034  0.16752502]
 [-0.52520067 -0.72250421  0.11259767]
 [-0.76830021  0.24452723 -0.42534148]]
 [14.49264657  3.92883644  0.72625043]
 [[-0.44571865 -0.46215842 -0.76664495]
 [-0.23882889  0.88677195 -0.39572247]
 [-0.86272571 -0.00671608  0.50562757]]
 [[1. 2. 3.]
 [1. 4. 2.]
 [4. 1. 7.]
 [5. 6. 8.]]