SVD 实现

机器学习相关——SVD分解：

http://www.cnblogs.com/luchen927/archive/2012/01/19/2321934.html

SVD python实现：

import numpy as np
from  numpy import dot

def loadData():
   return [[1,1,1,0,0],
            [2,2,2,0,0],
            [3,3,3,0,0],
            [5,5,3,2,2],
             [0,0,0,3,3],
             [0,0,0,6,6]]  

data=loadData()  

u,sigma,v=linalg.svd(data)  

print sigma
print u
print v 

def restore(sigma, u, v, k):          #  取k个特征，对矩阵重新进行计算
    m = len(u)
    n = len(v)
    b = np.zeros((m, n))
    for j in range(k-1):
        print "j=" ,j
        for i in range(m):
            print "i=",i
            print "sigma[j]",sigma[j]
            print "u[i][j]",u[i][j]
            print "v[j]",v[j]
            b[i] += sigma[j] * u[i][j] * v[j]
            print b
    return b  

result=restore(sigma, u, v, 3)
print result 

def restore2(sigma, u, v, k):
  b = np.zeros((k, k))
  for i in range(k):
    b[i][i] = sigma[i]
    out = dot(dot(u[:,:k],b),v[:k])
  return out

result2=restore2(sigma,u,v,2)
print result2