Python中利用svd进行矩阵分解和重构原始矩阵??

 1 # 创建数据集,5*7的矩阵
 2 def loadExData():
 3     return [[1,1,1,0,0],
 4             [2,2,2,0,0],
 5             [1,1,1,0,0],
 6             [5,5,5,0,0],
 7             [1,1,0,2,2],
 8             [0,0,0,3,3],
 9             [0,0,0,1,1]];
10 # 对矩阵进行SVD分解
11 from numpy import *;
12 def svd_():
13     Data=loadExData();
14     U,Sigma,VT=linalg.svd(Data);    
15     print(‘SVD分解Sigma的结果为:‘,Sigma);
16     return U,Sigma,VT;
17 """
18 array([  9.72140007e+00,   5.29397912e+00,   6.84226362e-01,
19          1.52344501e-15,   2.17780259e-16])
20 可以看到最后两个值很小,于是就可以将最后两个值去掉了
21 """
22 # 近似重构原始矩阵
23 def reconstructMat():
24     U,Sigma,VT=svd_();
25     Sig3=mat([[Sigma[0],0,0],[0,Sigma[1],0],[0,0,Sigma[2]]]);
26     reconMat=U[:,:3]*Sig3*VT[:3,:];
27     return reconMat;

 1 >>> reconMat
 2 matrix([[  1.00000000e+00,   1.00000000e+00,   1.00000000e+00,
 3           -1.51788304e-17,  -1.02999206e-17],
 4         [  2.00000000e+00,   2.00000000e+00,   2.00000000e+00,
 5            1.73472348e-18,   1.12757026e-17],
 6         [  1.00000000e+00,   1.00000000e+00,   1.00000000e+00,
 7            7.61977287e-16,   7.66747776e-16],
 8         [  5.00000000e+00,   5.00000000e+00,   5.00000000e+00,
 9            6.59194921e-17,   9.02056208e-17],
10         [  1.00000000e+00,   1.00000000e+00,  -7.21644966e-16,
11            2.00000000e+00,   2.00000000e+00],
12         [  1.66533454e-16,   1.30451205e-15,  -8.88178420e-16,
13            3.00000000e+00,   3.00000000e+00],
14         [  6.24500451e-17,   4.57966998e-16,  -3.33066907e-16,
15            1.00000000e+00,   1.00000000e+00]])

1 >>> loadExData()
2 [[1, 1, 1, 0, 0],
   [2, 2, 2, 0, 0], 
   [1, 1, 1, 0, 0], 
   [5, 5, 5, 0, 0], 
   [1, 1, 0, 2, 2], 
   [0, 0, 0, 3, 3], 
   [0, 0, 0, 1, 1]]