1.将代码拷贝到F:\studio\MachineLearningInAction\ch14下
2.启动ipython
3.在ipython中改变工作目录到F:\studio\MachineLearningInAction\ch14
In [17]: cd F:\\studio\\MachineLearningInAction\\ch14 F:\studio\MachineLearningInAction\ch14
4.在工作目录下新建一个svdRec.py文件并加入如下代码：
from numpy import *
from numpy import linalg as la
def loadExData():
return[[0, 0, 0, 2, 2],
[0, 0, 0, 3, 3],
[0, 0, 0, 1, 1],
[1, 1, 1, 0, 0],
[2, 2, 2, 0, 0],
[5, 5, 5, 0, 0],
[1, 1, 1, 0, 0]]
5.进行SVD分解并验证分解结果：
In [18]: import svdRec
In [19]: Data=svdRec.loadExData()
In [20]: U,Sigma,VT=linalg.svd(Data)
In [21]: Sigma
Out[21]:
array([ 9.64365076e+00, 5.29150262e+00, 9.11145502e-16,
1.40456183e-16, 3.09084552e-17])
In [22]: Sig2=mat([[Sigma[0],0],[0,Sigma[2]]])
In [23]: Sig2
Out[23]:
matrix([[ 9.64365076e+00, 0.00000000e+00],
[ 0.00000000e+00, 9.11145502e-16]])
In [24]: Sig2=mat([[Sigma[0],0],[0,Sigma[1]]])
In [25]: Sig2
Out[25]:
matrix([[ 9.64365076, 0. ],
[ 0. , 5.29150262]])
In [26]: U[:,:2]*Sig2*VT[:2,:]
Out[26]:
matrix([[ -1.36157966e-16, -8.59140046e-16, -8.59140046e-16,
2.00000000e+00, 2.00000000e+00],
[ 7.22982080e-16, -3.61491040e-16, -3.61491040e-16,
3.00000000e+00, 3.00000000e+00],
[ 2.40994027e-16, -1.20497013e-16, -1.20497013e-16,
1.00000000e+00, 1.00000000e+00],
[ 1.00000000e+00, 1.00000000e+00, 1.00000000e+00,
-8.60707644e-18, -8.60707644e-18],
[ 2.00000000e+00, 2.00000000e+00, 2.00000000e+00,
-1.72141529e-17, -1.72141529e-17],
[ 5.00000000e+00, 5.00000000e+00, 5.00000000e+00,
-1.39716789e-16, -1.39716789e-16],
[ 1.00000000e+00, 1.00000000e+00, 1.00000000e+00,
-8.60707644e-18, -8.60707644e-18]])
可以看出，U[:,:2]*Sig2*VT[:2,:]是对原来的Data矩阵的一个非常好的近似。
6.在svdRec.py中加入如下代码:
def ecludSim(inA,inB):
return 1.0/(1.0 + la.norm(inA - inB))
def pearsSim(inA,inB):
if len(inA) < 3 : return 1.0
return 0.5+0.5*corrcoef(inA, inB, rowvar = 0)[0][1]
def cosSim(inA,inB):
num = float(inA.T*inB)
denom = la.norm(inA)*la.norm(inB)
return 0.5+0.5*(num/denom)
上述代码定义了三种不同的相似度量
7.利用朴素的基于相似度的推荐方法建议推荐结果
In [44]: reload(svdRec)
Out[44]: <module ‘svdRec‘ from ‘svdRec.py‘>
In [45]: myMat=mat(svdRec.loadExData())
In [46]: myMat
Out[46]:
matrix([[0, 0, 0, 2, 2],
[0, 0, 0, 3, 3],
[0, 0, 0, 1, 1],
[1, 1, 1, 0, 0],
[2, 2, 2, 0, 0],
[5, 5, 5, 0, 0],
[1, 1, 1, 0, 0]])
In [47]: myMat[0,1]=myMat[0,0]=myMat[1,0]=myMat[2,0]=4
In [48]: myMat[3,3]=2
In [49]: myMat
Out[49]:
matrix([[4, 4, 0, 2, 2],
[4, 0, 0, 3, 3],
[4, 0, 0, 1, 1],
[1, 1, 1, 2, 0],
[2, 2, 2, 0, 0],
[5, 5, 5, 0, 0],
[1, 1, 1, 0, 0]])
In [50]: svdRec.recommend(myMat,2)
the 1 and 0 similarity is: 1.000000
the 1 and 3 similarity is: 0.928746
the 1 and 4 similarity is: 1.000000
the 2 and 0 similarity is: 1.000000
the 2 and 3 similarity is: 1.000000
the 2 and 4 similarity is: 0.000000
Out[50]: [(2, 2.5), (1, 2.0243290220056256)]
In [53]: svdRec.recommend(myMat,2,simMeas=svdRec.ecludSim)
the 1 and 0 similarity is: 1.000000
the 1 and 3 similarity is: 0.309017
the 1 and 4 similarity is: 0.333333
the 2 and 0 similarity is: 1.000000
the 2 and 3 similarity is: 0.500000
the 2 and 4 similarity is: 0.000000
Out[53]: [(2, 3.0), (1, 2.8266504712098603)]
In [54]: svdRec.recommend(myMat,2,simMeas=svdRec.pearsSim)
the 1 and 0 similarity is: 1.000000
the 1 and 3 similarity is: 1.000000
the 1 and 4 similarity is: 1.000000
the 2 and 0 similarity is: 1.000000
the 2 and 3 similarity is: 1.000000
the 2 and 4 similarity is: 0.000000
Out[54]: [(2, 2.5), (1, 2.0)]
8.利用SVD提高推荐的效果
在svdRec代码中个加入如下代码:
def loadExData2():
return[[0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 5],
[0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 3],
[0, 0, 0, 0, 4, 0, 0, 1, 0, 4, 0],
[3, 3, 4, 0, 0, 0, 0, 2, 2, 0, 0],
[5, 4, 5, 0, 0, 0, 0, 5, 5, 0, 0],
[0, 0, 0, 0, 5, 0, 1, 0, 0, 5, 0],
[4, 3, 4, 0, 0, 0, 0, 5, 5, 0, 1],
[0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4],
[0, 0, 0, 2, 0, 2, 5, 0, 0, 1, 2],
[0, 0, 0, 0, 5, 0, 0, 0, 0, 4, 0],
[1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0]]
上面的矩阵比较稀疏。现在计算该矩阵进行SVD分解需要多少维特征
In [57]: reload(svdRec)
Out[57]: <module ‘svdRec‘ from ‘svdRec.py‘>
In [58]: U,Sigma,VT=la.svd(mat(svdRec.loadExData2()))
In [59]: Sigma
Out[59]:
array([ 15.77075346, 11.40670395, 11.03044558, 4.84639758,
3.09292055, 2.58097379, 1.00413543, 0.72817072,
0.43800353, 0.22082113, 0.07367823])
In [60]: mat(svdRec.loadExData2())
Out[60]:
matrix([[0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 5],
[0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 3],
[0, 0, 0, 0, 4, 0, 0, 1, 0, 4, 0],
[3, 3, 4, 0, 0, 0, 0, 2, 2, 0, 0],
[5, 4, 5, 0, 0, 0, 0, 5, 5, 0, 0],
[0, 0, 0, 0, 5, 0, 1, 0, 0, 5, 0],
[4, 3, 4, 0, 0, 0, 0, 5, 5, 0, 1],
[0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 4],
[0, 0, 0, 2, 0, 2, 5, 0, 0, 1, 2],
[0, 0, 0, 0, 5, 0, 0, 0, 0, 4, 0],
[1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0]])
In [61]: Sig2=Sigma**2
In [62]: Sig2
Out[62]:
array([ 2.48716665e+02, 1.30112895e+02, 1.21670730e+02,
2.34875695e+01, 9.56615756e+00, 6.66142570e+00,
1.00828796e+00, 5.30232598e-01, 1.91847092e-01,
4.87619735e-02, 5.42848136e-03])
In [63]: sum(Sig2)
Out[63]: 541.99999999999955
In [64]: sum(Sig2)*0.9
Out[64]: 487.79999999999961
In [65]: sum(Sig2[:2])
Out[65]: 378.82955951135784
In [66]: sum(Sig2[:3])
Out[66]: 500.50028912757921
9.基于SVD进行评分：
在svdRec中加入如下代码:
def svdEst(dataMat, user, simMeas, item):
n = shape(dataMat)[1]
simTotal = 0.0; ratSimTotal = 0.0
U,Sigma,VT = la.svd(dataMat)
Sig4 = mat(eye(4)*Sigma[:4]) #arrange Sig4 into a diagonal matrix
xformedItems = dataMat.T * U[:,:4] * Sig4.I #create transformed items
for j in range(n):
userRating = dataMat[user,j]
if userRating == 0 or j==item: continue
similarity = simMeas(xformedItems[item,:].T, xformedItems[j,:].T)
print ‘the %d and %d similarity is: %f‘ % (item, j, similarity)
simTotal += similarity
ratSimTotal += similarity * userRating
if simTotal == 0: return 0
else: return ratSimTotal/simTotal
它定义了基于SVD的相似度评分
10.测试效果
In [69]: myMat=mat(svdRec.loadExData2()) In [70]: svdRec.recommend(myMat,1,estMethod=svdRec.svdEst) the 0 and 3 similarity is: 0.490950 the 0 and 5 similarity is: 0.484274 the 0 and 10 similarity is: 0.512755 the 1 and 3 similarity is: 0.491294 the 1 and 5 similarity is: 0.481516 the 1 and 10 similarity is: 0.509709 the 2 and 3 similarity is: 0.491573 the 2 and 5 similarity is: 0.482346 the 2 and 10 similarity is: 0.510584 the 4 and 3 similarity is: 0.450495 the 4 and 5 similarity is: 0.506795 the 4 and 10 similarity is: 0.512896 the 6 and 3 similarity is: 0.743699 the 6 and 5 similarity is: 0.468366 the 6 and 10 similarity is: 0.439465 the 7 and 3 similarity is: 0.482175 the 7 and 5 similarity is: 0.494716 the 7 and 10 similarity is: 0.524970 the 8 and 3 similarity is: 0.491307 the 8 and 5 similarity is: 0.491228 the 8 and 10 similarity is: 0.520290 the 9 and 3 similarity is: 0.522379 the 9 and 5 similarity is: 0.496130 the 9 and 10 similarity is: 0.493617 Out[70]: [(4, 3.3447149384692283), (7, 3.3294020724526971), (9, 3.3281008763900695)] In [71]: svdRec.recommend(myMat,1,estMethod=svdRec.svdEst,simMeas=svdRec.pearsSim) the 0 and 3 similarity is: 0.341942 the 0 and 5 similarity is: 0.124132 the 0 and 10 similarity is: 0.116698 the 1 and 3 similarity is: 0.345560 the 1 and 5 similarity is: 0.126456 the 1 and 10 similarity is: 0.118892 the 2 and 3 similarity is: 0.345149 the 2 and 5 similarity is: 0.126190 the 2 and 10 similarity is: 0.118640 the 4 and 3 similarity is: 0.450126 the 4 and 5 similarity is: 0.528504 the 4 and 10 similarity is: 0.544647 the 6 and 3 similarity is: 0.923822 the 6 and 5 similarity is: 0.724840 the 6 and 10 similarity is: 0.710896 the 7 and 3 similarity is: 0.319482 the 7 and 5 similarity is: 0.118324 the 7 and 10 similarity is: 0.113370 the 8 and 3 similarity is: 0.334910 the 8 and 5 similarity is: 0.119673 the 8 and 10 similarity is: 0.112497 the 9 and 3 similarity is: 0.566918 the 9 and 5 similarity is: 0.590049 the 9 and 10 similarity is: 0.602380 Out[71]: [(4, 3.3469521867021736), (9, 3.3353796573274703), (6, 3.307193027813037)] In [72]:
时间： 2024-10-09 00:59:56