基于物品—SVD餐馆评分估计值
Posted SongpingWang
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文章目录
1 导入模块 并 创建数据集
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]]
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]]
def loadExData3():
# 利用SVD提高推荐效果，菜肴矩阵
return[[2, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5],
[0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0],
[3, 3, 4, 0, 3, 0, 0, 2, 2, 0, 0],
[5, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0],
[4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 5],
[0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4],
[0, 0, 0, 0, 0, 0, 5, 0, 0, 5, 0],
[0, 0, 0, 3, 0, 0, 0, 0, 4, 5, 0],
[1, 1, 2, 1, 1, 2, 1, 0, 4, 5, 0]]
2 定义距离函数
def ecludSim(inA,inB): #计算欧几里得相似度（范数）
return 1.0/(1.0 + la.norm(inA - inB))
def pearsSim(inA,inB): #皮尔森相似度
if len(inA) < 3 : return 1.0
return 0.5+0.5*corrcoef(inA, inB, rowvar = 0)[0][1]
def cosSim(inA,inB): #cos相似度
num = float(inA.T*inB)
denom = la.norm(inA)*la.norm(inB)
return 0.5+0.5*(num/denom)
3 基于物品相似度, 计算用户对物体的评分估计值
def standEst(dataMat, user, simMeas, item): #estimate：评估器（数据矩阵，用户，相似度，菜种类）
n = shape(dataMat)[1] #取列
simTotal = 0.0; ratSimTotal = 0.0
for j in range(n):
userRating = dataMat[user,j]
if userRating == 0: continue
overLap = nonzero(logical_and(dataMat[:,item].A>0, \\
dataMat[:,j].A>0))[0] #如果第j个菜和item同时被人吃（返回bool的Ture）
if len(overLap) == 0: similarity = 0
else: similarity = simMeas(dataMat[overLap,item], \\
dataMat[overLap,j])
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
4 基于 SVD, 计算用户对物体的评分估计值
def svdEst(dataMat, user, simMeas, item):
n = shape(dataMat)[1]
simTotal = 0.0; ratSimTotal = 0.0
U,Sigma,VT = la.svd(dataMat)
# 在SVD分解之后，我们只利用包含了90%能量值的奇异值，
Sig4 = mat(eye(4)*Sigma[:4]) # eye生成单位矩阵，整个语句将奇异值变为矩阵的形式
# 利用U矩阵将物品转换到低维空间中，构建转换后的物品(物品+4个主要的特征)
xformedItems = dataMat.T * U[:,:4] * Sig4.I #变换坐标后的形式
for j in range(n): # #变换坐标后的形式 # 列数 现在变成了 行数
userRating = dataMat[user,j]
if userRating == 0 or j==item: continue
similarity = simMeas(xformedItems[item,:].T,\\
xformedItems[j,:].T) # 因为矩阵已经转置了，所以每行代表商品
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
def recommend(dataMat, user, N=3, simMeas=cosSim, estMethod=standEst):
unratedItems = nonzero(dataMat[user,:].A==0)[1]#find unrated items
if len(unratedItems) == 0: return you rated everything
itemScores = []
for item in unratedItems:
estimatedScore = estMethod(dataMat, user, simMeas, item)
itemScores.append((item, estimatedScore))
return sorted(itemScores, key=lambda jj: jj[1], reverse=True)[:N]
def printMat(inMat, thresh=0.8):
for i in range(32):
for k in range(32):
if float(inMat[i,k]) > thresh:
print(1, end=)
else: print(0, end=)
print()
myMat = mat(loadExData3())
rec_res = recommend(myMat, 1, estMethod=svdEst)
print(rec_res)
rec_res = recommend(myMat, 1, estMethod=svdEst, simMeas=pearsSim)
print(rec_res)
rec_res = recommend(myMat, 2)
print(rec_res)
# 注释: loadExData3函数是新增的
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