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)

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脚本之家。