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#!usr/bin/env python#_*_ coding:utf-8 _*_import pandas as pdimport numpy as npimport matplotlib.pyplot as plt#如果一个旅游网站里面有100000个注册用户，以及100个注册酒店，网站有用户通过本网站点击酒店页面的#记录数据信息A=Aij 100000*100 Aij表示第i个用户点击j酒店的次数#Q1:如何评价酒店之间的相似度#Q2:给定一个酒店，请找出与它最相似的其他几个酒店#Q3:如何要给酒店分类，有什么办法？#prepare data set,suppose there are 5 types of hotels 纬度评分generatorNum=5 #5hotelNum=100 #100customerNum=100000 #100000#10000用户个对五个纬度的侧重点的评分generators=np.random.randint(5,size=(customerNum,generatorNum))
print(generators)#酒店在各个纬度为评分hotelcomp=np.random.random(size=(generatorNum,hotelNum))-0.5# 0.5出现负值print(hotelcomp)#.dot矩阵运算，生成顾客对酒店评分hotelRating=pd.DataFrame(generators.dot(hotelcomp),index=['c%.6d'%i for i in range(customerNum)],columns=['hotel_%.3d'%j for j in range(100)]).astype(int)#data z-score公式def normalize(s):
if s.std()>1e-6: #**乘方,就散标准分数z-score，用来算离数据中心的偏差的,https://www.zhihu.com/question/21600637
return(s-s.mean())*s.std()**(-1) else: return (s-s.mean())#如何评价酒店之间的相似度？#data to z-scorehotelRating_norm=hotelRating.apply(normalize)
print('hotelRating_norm\n{}'.format(hotelRating_norm))
print(type(hotelRating_norm))#计算协方差hotelRating_norm_corr=hotelRating_norm.cov()
print('hotelRating_norm_corr\n{}'.format(hotelRating_norm_corr))#SVD，即奇异值分解u,s,v=np.linalg.svd(hotelRating_norm_corr)#碎石图确定分类，测试时是5print('u\n{}'.format(u))
print(s)
plt.plot(s,'o')
plt.title("singular value spectrum")
plt.show()
#截取SVD纬度u_short = u[:,:5]
v_short = v[:5,:]
s_short = s[:5]print('u,s,v,short{}'.format(u_short,v_short,s_short))#numpy.diag()创建一个对角矩阵hotelRating_norm_corr_rebuild=pd.DataFrame(u_short.dot(np.diag(s_short).dot(v_short)),index=hotelRating_norm_corr.index,columns=hotelRating_norm_corr.keys())#get the top components ,np.power数组的元素分别求n次方top_component=hotelRating_norm.dot(u_short).dot(np.diag(np.power(s_short,-0.5)))#classfication of each hotelhotel_ind = 3rating = hotelRating_norm.loc[:,'hotel_%.3d'%hotel_ind]print ("classification of the %dth hotel"%hotel_ind,top_component.T.dot(rating)/customerNum)结果 
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