基于baseline、svd和stochastic gradient descent的个性化推荐系统

文章主要介绍的是koren 08年发的论文[1],  2.3部分内容（其余部分会陆续补充上来）。
koren论文中用到netflix 数据集， 过于大， 在普通的pc机上运行时间很长很长。考虑到写文章目地主要是已介绍总结方法为主，所以采用Movielens 数据集。

变量介绍

部分变量介绍可以参看《基于baseline和stochastic gradient descent的个性化推荐系统》

文章中，将介绍两种方法实现的简易个性化推荐系统，用RMSE评价标准，对比这两个方法的实验结果。

（1） svd + stochstic gradient descent 方法来实现系统。

（2） baseline + svd + stochastic gradient descent 方法来实现系统。

注：

方法1： svd + stochastic gradient descent

svd:

cost  function:

梯度变化（利用stochastic gradient descent算法使上述的目标函数值，在设定的迭代次数内，降到最小）

具体代码实现：

'''''
Created on Dec 13, 2012 

@Author: Dennis Wu
@E-mail: hansel.zh@gmail.com
@Homepage: http://blog.csdn.net/wuzh670 

Data set download from : http://www.grouplens.org/system/files/ml-100k.zip
'''  

from operator import itemgetter, attrgetter
from math import sqrt
import random  

def load_data():  

    train = {}
    test = {}
    filename_train = 'data/ua.base'
    filename_test = 'data/ua.test'  

    for line in open(filename_train):
        (userId, itemId, rating, timestamp) = line.strip().split('\t')
        train.setdefault(userId,{})
        train[userId][itemId] = float(rating)  

    for line in open(filename_test):
        (userId, itemId, rating, timestamp) = line.strip().split('\t')
        test.setdefault(userId,{})
        test[userId][itemId] = float(rating)  

    return train, test  

def calMean(train):
    stat = 0
    num = 0
    for u in train.keys():
        for i in train[u].keys():
            stat += train[u][i]
            num += 1
    mean = stat*1.0/num
    return mean  

def initialFeature(feature, userNum, movieNum):  

    random.seed(0)
    user_feature = {}
    item_feature = {}
    i = 1
    while i < (userNum+1):
        si = str(i)
        user_feature.setdefault(si,{})
        j = 1
        while j < (feature+1):
            sj = str(j)
            user_feature[si].setdefault(sj,random.uniform(0,1))
            j += 1
        i += 1  

    i = 1
    while i < (movieNum+1):
        si = str(i)
        item_feature.setdefault(si,{})
        j = 1
        while j < (feature+1):
            sj = str(j)
            item_feature[si].setdefault(sj,random.uniform(0,1))
            j += 1
        i += 1
    return user_feature, item_feature  

def svd(train, test, userNum, movieNum, feature, user_feature, item_feature):  

    gama = 0.02
    lamda = 0.3
    slowRate = 0.99
    step = 0
    preRmse = 1000000000.0
    nowRmse = 0.0  

    while step < 100:
        rmse = 0.0
        n = 0
        for u in train.keys():
            for i in train[u].keys():
                pui = 0
                k = 1
                while k < (feature+1):
                    sk = str(k)
                    pui += user_feature[u][sk] * item_feature[i][sk]
                    k += 1
                eui = train[u][i] - pui
                rmse += pow(eui,2)
                n += 1
                k = 1
                while k < (feature+1):
                    sk = str(k)
                    user_feature[u][sk] += gama*(eui*item_feature[i][sk] - lamda*user_feature[u][sk])
                    item_feature[i][sk] += gama*(eui*user_feature[u][sk] - lamda**item_feature[i][sk])
                    k += 1  

        nowRmse = sqrt(rmse*1.0/n)
        print 'step: %d      Rmse: %s' % ((step+1), nowRmse)
        if (nowRmse < preRmse):
            preRmse = nowRmse  

        gama *= slowRate
        step += 1  

    return user_feature, item_feature  

def calRmse(test, user_feature, item_feature, feature):  

    rmse = 0.0
    n = 0
    for u in test.keys():
        for i in test[u].keys():
            pui = 0
            k = 1
            while k < (feature+1):
                sk = str(k)
                pui += user_feature[u][sk] * item_feature[i][sk]
                k += 1
            eui = pui - test[u][i]
            rmse += pow(eui,2)
            n += 1
    rmse = sqrt(rmse*1.0 / n)
    return rmse;  

if __name__ == "__main__":  

    # load data
    train, test = load_data()
    print 'load data success'  

    # initial user and item feature, respectly
    user_feature, item_feature = initialFeature(100, 943, 1682)
    print 'initial user and item feature, respectly success'  

    # baseline + svd + stochastic gradient descent
    user_feature, item_feature = svd(train, test, 943, 1682, 100, user_feature, item_feature)
    print 'svd + stochastic gradient descent success'  

    # compute the rmse of test set
    print 'the Rmse of test test is: %s' % calRmse(test, user_feature, item_feature, 100)
 

方法2：baseline + svd + stochastic gradient descent

baseline + svd:

object function:

梯度变化（利用stochastic gradient descent算法使上述的目标函数值，在设定的迭代次数内，降到最小）

方法2： 具体代码实现

'''''
Created on Dec 13, 2012 

@Author: Dennis Wu
@E-mail: hansel.zh@gmail.com
@Homepage: http://blog.csdn.net/wuzh670 

Data set download from : http://www.grouplens.org/system/files/ml-100k.zip
'''  

from operator import itemgetter, attrgetter
from math import sqrt
import random  

def load_data():  

    train = {}
    test = {}
    filename_train = 'data/ua.base'
    filename_test = 'data/ua.test'  

    for line in open(filename_train):
        (userId, itemId, rating, timestamp) = line.strip().split('\t')
        train.setdefault(userId,{})
        train[userId][itemId] = float(rating)  

    for line in open(filename_test):
        (userId, itemId, rating, timestamp) = line.strip().split('\t')
        test.setdefault(userId,{})
        test[userId][itemId] = float(rating)  

    return train, test  

def calMean(train):
    stat = 0
    num = 0
    for u in train.keys():
        for i in train[u].keys():
            stat += train[u][i]
            num += 1
    mean = stat*1.0/num
    return mean  

def initialBias(train, userNum, movieNum, mean):  

    bu = {}
    bi = {}
    biNum = {}
    buNum = {}  

    u = 1
    while u < (userNum+1):
        su = str(u)
        for i in train[su].keys():
            bi.setdefault(i,0)
            biNum.setdefault(i,0)
            bi[i] += (train[su][i] - mean)
            biNum[i] += 1
        u += 1  

    i = 1
    while i < (movieNum+1):
        si = str(i)
        biNum.setdefault(si,0)
        if biNum[si] >= 1:
            bi[si] = bi[si]*1.0/(biNum[si]+25)
        else:
            bi[si] = 0.0
        i += 1  

    u = 1
    while u < (userNum+1):
        su = str(u)
        for i in train[su].keys():
            bu.setdefault(su,0)
            buNum.setdefault(su,0)
            bu[su] += (train[su][i] - mean - bi[i])
            buNum[su] += 1
        u += 1  

    u = 1
    while u < (userNum+1):
        su = str(u)
        buNum.setdefault(su,0)
        if buNum[su] >= 1:
            bu[su] = bu[su]*1.0/(buNum[su]+10)
        else:
            bu[su] = 0.0
        u += 1  

    return bu,bi  

def initialFeature(feature, userNum, movieNum):  

    random.seed(0)
    user_feature = {}
    item_feature = {}
    i = 1
    while i < (userNum+1):
        si = str(i)
        user_feature.setdefault(si,{})
        j = 1
        while j < (feature+1):
            sj = str(j)
            user_feature[si].setdefault(sj,random.uniform(0,1))
            j += 1
        i += 1  

    i = 1
    while i < (movieNum+1):
        si = str(i)
        item_feature.setdefault(si,{})
        j = 1
        while j < (feature+1):
            sj = str(j)
            item_feature[si].setdefault(sj,random.uniform(0,1))
            j += 1
        i += 1
    return user_feature, item_feature  

def svd(train, test, mean, userNum, movieNum, feature, user_feature, item_feature, bu, bi):  

    gama = 0.02
    lamda = 0.3
    slowRate = 0.99
    step = 0
    preRmse = 1000000000.0
    nowRmse = 0.0  

    while step < 100:
        rmse = 0.0
        n = 0
        for u in train.keys():
            for i in train[u].keys():
                pui = 1.0 * (mean + bu[u] + bi[i])
                k = 1
                while k < (feature+1):
                    sk = str(k)
                    pui += user_feature[u][sk] * item_feature[i][sk]
                    k += 1
                eui = train[u][i] - pui
                rmse += pow(eui,2)
                n += 1
                bu[u] += gama * (eui - lamda * bu[u])
                bi[i] += gama * (eui - lamda * bi[i])
                k = 1
                while k < (feature+1):
                    sk = str(k)
                    user_feature[u][sk] += gama*(eui*item_feature[i][sk] - lamda*user_feature[u][sk])
                    item_feature[i][sk] += gama*(eui*user_feature[u][sk] - lamda*item_feature[i][sk])
                    k += 1  

        nowRmse = sqrt(rmse*1.0/n)
        print 'step: %d      Rmse: %s' % ((step+1), nowRmse)
        if (nowRmse < preRmse):
            preRmse = nowRmse  

        gama *= slowRate
        step += 1
    return user_feature, item_feature, bu, bi  

def calRmse(test, bu, bi, user_feature, item_feature, mean, feature):  

    rmse = 0.0
    n = 0
    for u in test.keys():
        for i in test[u].keys():
            pui = 1.0 * (mean + bu[u] + bi[i])
            k = 1
            while k < (feature+1):
                sk = str(k)
                pui += user_feature[u][sk] * item_feature[i][sk]
                k += 1
            eui = pui - test[u][i]
            rmse += pow(eui,2)
            n += 1
    rmse = sqrt(rmse*1.0 / n)
    return rmse;  

if __name__ == "__main__":  

    # load data
    train, test = load_data()
    print 'load data success'  

    # Calculate overall mean rating
    mean = calMean(train)
    print 'Calculate overall mean rating success'  

    # initial user and item Bias, respectly
    bu, bi = initialBias(train, 943, 1682, mean)
    print 'initial user and item Bias, respectly success'  

    # initial user and item feature, respectly
    user_feature, item_feature = initialFeature(100, 943, 1682)
    print 'initial user and item feature, respectly success'  

    # baseline + svd + stochastic gradient descent
    user_feature, item_feature, bu, bi = svd(train, test, mean, 943, 1682, 100, user_feature, item_feature, bu, bi)
    print 'baseline + svd + stochastic gradient descent success'  

    # compute the rmse of test set
    print 'the Rmse of test test is: %s' % calRmse(test, bu, bi, user_feature, item_feature, mean, 100)  

实验参数设置：

(gama = 0.02  lamda =0.3)

feature = 100 maxstep = 100 slowRate = 0.99(随着迭代次数增加，梯度下降幅度越来越小)

方法1结果：Rmse of test set : 1.00422938926

方法2结果：Rmse of test set : 0.963661477881

REFERENCES

1.Y. Koren. Factorization Meets the Neighborhood: a Multifaceted Collaborative Filtering Model. Proc. 14th ACM SIGKDD Int. Conf. On Knowledge Discovery and Data Mining  (KDD’08), pp. 426–434, 2008.

2. Y.Koren.  The BellKor Solution to the Netflix Grand Prize  2009