基于baseline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],  2.1 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。

要用到的变量介绍：

Baseline estimates

     

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）

系统评判标准：

参数设置：

迭代次数maxStep = 100, 学习速率（梯度变化速率）取0.99  还有的其他参数设置参考引用论文[2]

具体的代码实现

'''''
Created on Dec 11, 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):
    sta = 0
    num = 0
    for u in train.keys():
        for i in train[u].keys():
            sta += train[u][i]
            num += 1
    mean = sta*1.0/num
    return mean  

def initialBias(train, userNum, movieNum):  

    mean = calMean(train)
    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,mean  

def sgd(train, test, userNum, movieNum):  

    bu, bi, mean = initialBias(train, userNum, movieNum)  

    alpha1 = 0.002
    beta1 = 0.1
    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])
                eui = train[u][i] - pui
                rmse += pow(eui,2)
                n += 1
                bu[u] += alpha1 * (eui - beta1 * bu[u])
                bi[i] += alpha1 * (eui - beta1 * bi[i])  

        nowRmse = sqrt(rmse*1.0/n)
        print 'step: %d      Rmse: %s' % ((step+1), nowRmse)
        if (nowRmse < preRmse):
            preRmse = nowRmse
        alpha1 *= slowRate
        step += 1
    return bu, bi, mean  

def calRmse(test, bu, bi, mean):  

    rmse = 0.0
    n = 0
    for u in test.keys():
        for i in test[u].keys():
            pui = 1.0 * (mean + bu[u] + bi[i])
            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()  

    # baseline + stochastic gradient descent
    bu, bi, mean = sgd(train, test, 943, 1682)  

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

实验结果

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