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