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 pdimport numpy as npimport 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)