基于隨機梯度下降的矩陣分解推薦算法

SVD是矩陣分解常用的方法，其原理為：矩陣M可以寫成矩陣A、B與C相乘得到，而B可以與A或者C合并，就變成了兩個元素M1與M2的矩陣相乘可以得到M。
矩陣分解推薦的思想就是基于此，將每個user和item的內(nèi)在feature構(gòu)成的矩陣分別表示為M1與M2，則內(nèi)在feature的乘積得到M；因此我們可以利用已有數(shù)據(jù)（user對item的打分）通過隨機梯度下降的方法計算出現(xiàn)有user和item最可能的feature對應(yīng)到的M1與M2（相當(dāng)于得到每個user和每個item的內(nèi)在屬性），這樣就可以得到通過feature之間的內(nèi)積得到user沒有打過分的item的分數(shù)。
本文所采用的數(shù)據(jù)是movielens中的數(shù)據(jù)，且自行切割成了train和test，但是由于數(shù)據(jù)量較大，沒有用到全部數(shù)據(jù)。

代碼如下：

[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): #求兩個dataframe的差集  
        df = pd.merge(left,right,how='left',on=on) #參數(shù)on指的是用于連接的列索引名稱  
        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]#得到的數(shù)據(jù)里面還有其他同列名的column  
        df.columns = left_columns # 重新定義columns  
        return df  
          
    def readfile(filepath): #讀取文件，同時得到訓(xùn)練集和測試集  
          
        pwd = os.getcwd()#返回當(dāng)前工程的工作目錄  
        os.chdir(os.path.dirname(filepath))  
        #os.path.dirname()獲得filepath文件的目錄；chdir()切換到filepath目錄下  
        initialData =  pd.read_csv(os.path.basename(filepath))  
        #basename()獲取指定目錄的相對路徑  
        os.chdir(pwd)#回到先前工作目錄下  
        predData = initialData.iloc[:,0:3] #將最后一列數(shù)據(jù)去掉  
        newIndexData = predData.drop_duplicates()  
        trainData = newIndexData.sample(axis=0,frac = 0.1) #90%的數(shù)據(jù)作為訓(xùn)練集  
        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 #隨機梯度下降中加入，防止更新過度  
        user = pd.DataFrame(train.userId.drop_duplicates(),columns=['userId']).reset_index(drop=True) #把在原來dataFrame中的索引重新設(shè)置，drop=True并拋棄  
      
        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) #構(gòu)造user和movie的特征向量集合  
        movieFeatures = np.random.rand(movieNum,features)  
        #假設(shè)每個user和每個movie有3個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') #重新設(shè)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中對應(yīng)uId的feature  
      
                u_m = train[train['userId'] == uId] #找到在train中userId點評過的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:\學(xué)習(xí)\研究生\推薦系統(tǒng)\ml-latest-small\ratings.csv"  
        train,test = readfile(filepath)  
        userFeaturesFrame,movieFeaturesFrame = getmodel(train)  
        result = evaluate(userFeaturesFrame,movieFeaturesFrame,test)  

在test中得到的結(jié)果為：

NAN則是訓(xùn)練集中沒有的數(shù)據(jù)