基于随机梯度下降的矩阵分解推荐算法（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：

# -*- 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)

在test中得到的结果为：

nan则是训练集中没有的数据

以上就是本文的全部内容，希望对大家的学习有所帮助，也希望大家多多支持。