基于随机梯度下降的矩阵分解推荐算法（python）_Python

SVD是矩阵分解常用的方法，其原理为：矩阵M可以写成矩阵A、B与C相乘得到，而B可以与A或者C合并，就变成了两个元素M1与M2的矩阵相乘可以得到M。

矩阵分解推荐的思想就是基于此，将每个user和item的内在feature构成的矩阵分别表示为M1与M2，则内在feature的乘积得到M；因此我们可以利用已有数据（user对item的打分）通过随机梯度下降的方法计算出现有user和item最可能的feature对应到的M1与M2（相当于得到每个user和每个item的内在属性），这样就可以得到通过feature之间的内积得到user没有打过分的item的分数。

本文所采用的数据是movielens中的数据，且自行切割成了train和test，但是由于数据量较大，没有用到全部数据。

代码如下：

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									# -*- coding: utf-8 -*-

									"""

									Created on Mon Oct 9 19:33:00 2017

									@author: wjw

									"""

									import pandas as pd

									import numpy as np

									import os

									def difference(left,right,on): #求两个dataframe的差集

									 df = pd.merge(left,right,how='left',on=on) #参数on指的是用于连接的列索引名称

									 left_columns = left.columns

									 col_y = df.columns[-1] # 得到最后一列

									 df = df[df[col_y].isnull()]#得到boolean的list

									 df = df.iloc[:,0:left_columns.size]#得到的数据里面还有其他同列名的column

									 df.columns = left_columns # 重新定义columns

									 return df

									def readfile(filepath): #读取文件，同时得到训练集和测试集

									 pwd = os.getcwd()#返回当前工程的工作目录

									 os.chdir(os.path.dirname(filepath))

									 #os.path.dirname()获得filepath文件的目录；chdir()切换到filepath目录下

									 initialData = pd.read_csv(os.path.basename(filepath))

									 #basename()获取指定目录的相对路径

									 os.chdir(pwd)#回到先前工作目录下

									 predData = initialData.iloc[:,0:3] #将最后一列数据去掉

									 newIndexData = predData.drop_duplicates()

									 trainData = newIndexData.sample(axis=0,frac = 0.1) #90%的数据作为训练集

									 testData = difference(newIndexData,trainData,['userId','movieId']).sample(axis=0,frac=0.1)

									 return trainData,testData

									def getmodel(train):

									 slowRate = 0.99

									 preRmse = 10000000.0

									 max_iter = 100

									 features = 3

									 lamda = 0.2

									 gama = 0.01 #随机梯度下降中加入，防止更新过度

									 user = pd.DataFrame(train.userId.drop_duplicates(),columns=['userId']).reset_index(drop=True) #把在原来dataFrame中的索引重新设置，drop=True并抛弃

									 movie = pd.DataFrame(train.movieId.drop_duplicates(),columns=['movieId']).reset_index(drop=True)

									 userNum = user.count().loc['userId'] #671

									 movieNum = movie.count().loc['movieId'] 

									 userFeatures = np.random.rand(userNum,features) #构造user和movie的特征向量集合

									 movieFeatures = np.random.rand(movieNum,features)

									 #假设每个user和每个movie有3个feature

									 userFeaturesFrame =user.join(pd.DataFrame(userFeatures,columns = ['f1','f2','f3']))

									 movieFeaturesFrame =movie.join(pd.DataFrame(movieFeatures,columns= ['f1','f2','f3']))

									 userFeaturesFrame = userFeaturesFrame.set_index('userId')

									 movieFeaturesFrame = movieFeaturesFrame.set_index('movieId') #重新设置index

									 for i in range(max_iter): 

									  rmse = 0

									  n = 0

									  for index,row in user.iterrows():

									   uId = row.userId

									   userFeature = userFeaturesFrame.loc[uId] #得到userFeatureFrame中对应uId的feature

									   u_m = train[train['userId'] == uId] #找到在train中userId点评过的movieId的data

									   for index,row in u_m.iterrows(): 

									    u_mId = int(row.movieId)

									    realRating = row.rating

									    movieFeature = movieFeaturesFrame.loc[u_mId] 

									    eui = realRating-np.dot(userFeature,movieFeature)

									    rmse += pow(eui,2)

									    n += 1

									    userFeaturesFrame.loc[uId] += gama * (eui*movieFeature-lamda*userFeature) 

									    movieFeaturesFrame.loc[u_mId] += gama*(eui*userFeature-lamda*movieFeature)

									  nowRmse = np.sqrt(rmse*1.0/n)

									  print('step:%f,rmse:%f'%((i+1),nowRmse))

									  if nowRmse<preRmse:

									   preRmse = nowRmse

									  elif nowRmse<0.5:

									   break

									  elif nowRmse-preRmse<=0.001:

									   break

									  gama*=slowRate

									 return userFeaturesFrame,movieFeaturesFrame

									def evaluate(userFeaturesFrame,movieFeaturesFrame,test):

									 test['predictRating']='NAN' # 新增一列

									 for index,row in test.iterrows(): 

									  print(index)

									  userId = row.userId

									  movieId = row.movieId

									  if userId not in userFeaturesFrame.index or movieId not in movieFeaturesFrame.index:

									   continue

									  userFeature = userFeaturesFrame.loc[userId]

									  movieFeature = movieFeaturesFrame.loc[movieId]

									  test.loc[index,'predictRating'] = np.dot(userFeature,movieFeature) #不定位到不能修改值

									 return test 

									if __name__ == "__main__":

									 filepath = r"E:\学习\研究生\推荐系统\ml-latest-small\ratings.csv"

									 train,test = readfile(filepath)

									 userFeaturesFrame,movieFeaturesFrame = getmodel(train)

									 result = evaluate(userFeaturesFrame,movieFeaturesFrame,test)