Python3《机器学习实战》代码笔记（十四）--- SVD算法
参考资料:
机器学习实战
'''
@version: 0.0.1
@Author: tqrs
@dev: python3 vscode
@Date: 2019-11-12 21:09:57
@LastEditTime: 2019-11-12 21:58:07
@FilePath: \\机器学习实战\\14-SVD算法\\SVD.py
@Descripttion: SVD是从有噪声数据中抽取相关特征,利用SVD来逼近矩阵并从中提取重要特征,通过保留矩阵80%~90%的能量,
就可以得到重要的特征并去掉噪声
'''
import numpy as np
def loadExData():
return [[0, 0, 0, 2, 2],
[0, 5, 0, 3, 3],
[0, 0, 0, 1, 1],
[1, 1, 1, 0, 0],
[2, 1, 2, 4, 0],
[5, 5, 5, 3, 0],
[1, 1, 1, 2, 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 ecludSim(inA, inB):
"""计算两个列向量的欧氏距离"""
return 1.0 / (1.0 + np.linalg.norm(inA - inB))
def pearsSim(inA, inB):
"""计算两个列向量的皮尔逊相关系数"""
if len(inA) < 3:
return 1.0
return 0.5 + 0.5 * np.corrcoef(inA, inB, rowvar=False)[0][1]
def cosSim(inA, inB):
"""计算两个列向量的是余弦相似度"""
num = float(inA.T * inB)
denom = np.linalg.norm(inA) * np.linalg.norm(inB)
return 0.5 + 0.5 * (num / denom)
def test_Sim():
"""测试三种距离算法"""
myDat = np.mat(loadExData())
ecl = ecludSim(myDat[:, 0], myDat[:, 4])
print(ecl)
cos = cosSim(myDat[:, 0], myDat[:, 4])
print(cos)
pear = pearsSim(myDat[:, 0], myDat[:, 4])
print(pear)
def standEst(dataMat, user, simMeas, item):
"""
[summary]:计算在给定相似度计算方法的 条件下，用户对物品的估计评分值
Arguments:
dataMat -- 数据集
user --
simMeas --
item --
Returns:
[type] -- [description]
"""
n = np.shape(dataMat)[1] # 行数
simTotal = 0.0
ratSimTotal = 0.0
for j in range(n):
userRating = dataMat[user, j]
if userRating == 0 or j == item:
continue
# 寻找两个用户都评级的物品
overlap = np.nonzero(
np.logical_and(dataMat[:, item].A > 0, dataMat[:, j].A > 0))[0]
# 没有任何重合元素,相似度为0
if len(overlap) == 0:
similarity = 0
else:
similarity = simMeas(dataMat[overlap, j], dataMat[overlap, item])
print('the {:d} and {:d} similarity is:{:.6f}'.format(
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):
"""
[summary]:
(1) 寻找用户没有评级的菜肴，即在用户－物品矩阵中的0值
(2) 在用户没有评级的所有物品中，对每个物品预计一个可能的评级分数。这就是说，我们认为用户可能会对物品的打分(这就是相似度计算的初衷)
(3) 对这些物品的评分从高到低进行排序，返回前N个物品
Arguments:
dataMat {[type]} -- [description]
user {[type]} -- [description]
Keyword Arguments:
N {int} -- [description] (default: {3})
simMeas {[type]} -- [description] (default: {cosSim})
estMethod {[type]} -- [description] (default: {standEst})
Returns:
[type] -- [description]
"""
# 寻找未评级物品
unratedItems = np.nonzero(dataMat[user, :].A == 0)[1]
if len(unratedItems) == 0:
return 'all rated'
itemScores = [(item, estMethod(dataMat, user, simMeas, item))
for item in unratedItems]
# itemScores = []
# for item in unratedItems:
# estimatedScore=estMethod(dataMat,user,simMeas,item)
# itemScores.append((item,estimatedScore))
# 寻找前N个未评级物品
return sorted(itemScores, key=lambda x: x[1], reverse=True)[:N]
def test_recommend():
myDat = np.mat(loadExData())
myDat[0, 1] = myDat[0, 0] = myDat[1, 0] = myDat[2, 0] = 4
myDat[3, 3] = 2
print(recommend(myDat, 2))
def svdEst(dataMat, user, simMeas, item):
"""
[summary]:数对给定用户给定物品构建了一个评分估计值
Arguments:
dataMat {[type]} -- [description]
user {[type]} -- [description]
simMeas {[type]} -- [description]
item {[type]} -- [description]
Returns:
[type] -- [description]
"""
# 行数
n = np.shape(dataMat)[1]
simTotal = 0.0
ratSimTotal = 0.0
# SVD分解
U, Sigma, VT = np.linalg.svd(dataMat)
# 构建对角矩阵,Sigma[:4]只包含90%能量值的奇异值
Sig4 = np.mat(np.eye(4) * Sigma[:4])
xfromedItems = dataMat.T * U[:, :4] * Sig4.I
for j in range(n):
userRating = dataMat[user, j]
if userRating == 0 or j == item:
continue
similarity = simMeas(xfromedItems[item, :].T, xfromedItems[j, :].T)
print('the {:d} and {:d} similarity is:{:.6f}'.format(
item, j, similarity))
simTotal += similarity
ratSimTotal += similarity * userRating
if simTotal == 0:
return 0
else:
return ratSimTotal / simTotal
def test_svdEst():
myDat = np.mat(loadExData2())
# print(recommend(myDat, 1, estMethod=svdEst))
print(recommend(myDat, 1, estMethod=svdEst, simMeas=pearsSim))
# 打印矩阵
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='') # 不换行
else:
print(0, end='')
print(' ')
def imgCompress(numSV=3, thresh=0.8):
myl = []
for line in open(r'14-SVD算法\0_5.txt').readlines():
newRow = []
for i in range(32):
newRow.append(int(line[i]))
myl.append(newRow)
myMat = np.mat(myl)
print("****original matrix******")
printMat(myMat, thresh)
U, Sigma, VT = np.linalg.svd(myMat)
SigRecon = np.mat(np.zeros((numSV, numSV)))
for k in range(numSV): # construct diagonal matrix from vector
SigRecon[k, k] = Sigma[k]
reconMat = U[:, :numSV] * SigRecon * VT[:numSV, :]
print("****reconstructed matrix using %d singular values******" % numSV)
printMat(reconMat, thresh)
if __name__ == '__main__':
# test_Sim()
# test_recommend()
# test_svdEst()
imgCompress(2)