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