矩阵奇异分解（SVD）应用

from sklearn import preprocessing
import matplotlib.image as mpimg # mpimg 用于读取图片
import numpy as np
import matplotlib.pyplot as plt
from PIL import Image
I = Image.open('222.jpg')
print I.size
L = I.convert('I')
im_array = np.array(L,dtype=float)

# 求特征值，特征向量
# 假定原始数一列是一条数据，一行是一个字段

varData = np.dot(im_array.T,im_array)
a,b = np.linalg.eig(varData)
# 取实数部分，计算机计算近似会产生复数，取实数部分，这点需要处理
a = np.real(a)
b = np.real(b)

# 对特征值降序排列
sorted_indices = np.argsort(-a)
k=11
# 切片取特征向量列向量
topk_evecs = b[:,sorted_indices[:k]]

b_normalized = preprocessing.normalize(topk_evecs.T, norm='l2').T
sigma = np.sqrt(a[sorted_indices[:k]])
Sigma = np.diag(1/sigma)
newdiag = np.diag(sigma)
u1=np.dot(data,np.dot(b_normalized[:,:k], Sigma))

newdata = np.dot(u1,np.dot(newdiag,b_normalized.T))
newdata = np.array(newdata,dtype=int)

fig = plt.figure("cat")
plt.imshow(newdata, cmap ='gray')
plt.axis('off')
plt.show()