基于随机梯度下降的矩阵分解推荐算法

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：

[python] view plain copy

    # -*- 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