PCA实现一个简单的酒店推荐系统（附Python源码）

import pandas as pd
import numpy as np
#prepare data set, suppose there are 5 types of hotels
generatorNum=5
hotelNum=100
customerNum=100000

generators = np.random.randint(5, size=(customerNum, generatorNum))
hotelComp=np.random.random(size=(generatorNum, hotelNum)) - 0.5
hotelRating = pd.DataFrame(generators.dot(hotelComp),index=['c%.6d'%i for i in range(100000)]
                          ,columns = ['hotel_%.3d'%j for j in range(100)]).astype(int)

def normalize(s):
    if s.std()>1e-6:
        return (s-s.mean())*s.std()**(-1)
    else:
        return (s-s.mean())

u,s,v = np.linalg.svd(hotelRating_norm_corr)

In [9]:
import matplotlib.pyplot as plt
plt.plot(s,'o')
plt.title("singular value spectrum")
plt.show()

In [10]:
u_short = u[:,:5]
v_short = v[:5,:]
s_short = s[:5]

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())

In [11]:
#get the top components
top_components = hotelRating_norm.dot(u_short).dot(np.diag(np.power(s_short,-0.5)))

In [12]:
#classfication of each hotel
hotel_ind = 30
rating = hotelRating_norm.loc[:,'hotel_%.3d'%hotel_ind]
print "classification of the %dth hotel"%hotel_ind
top_components.T.dot(rating)/customerNum

classification of the 30th hotel
0    0.136138
1    0.179586
2   -0.071347
3   -0.384475
4    0.647324