基于相似性随时间衰减的矩阵分解算法

Matrix Factorization Algorithm Based on Similarity Decaying with Time

近年来时间信息越来越多的被应用到推荐系统中,但是大部分研究很少把相似性随时间的衰减融入到矩阵分解当中.用户近期的行为相比用户很久之前的行为,更能体现用户现在的兴趣.因此提出一种融合相似性衰减的矩阵分解算法,本算法把时间信息融入到相似性的计算当中,通过基于时间的协同过滤算法计算用户-用户相似性和物品-物品的相似性,并把此相似性的值作为误差函数的初始值.然后利用矩阵分解的方法计算出用户-用户,物品-物品之间的相似性,并把此相似性的值作为预测值.最后,我们利用初始值和预测值的差来构建误差函数.为了最小化误差函数,我们利用随机梯度下降法,进行迭代训练模型.在Movie Lens上的实验结果表明,提出的推荐算法在一定程度上提高了推荐结果的准确性.

In recent years,temporal information has been integrated into recommender systems. But in most studies,the phenomenon of similarity decaying with time is rarely considered in matrix factorization algorithm. The user＇s recent behavior can better reflect his interests,comparing with his past behaviors. Therefore a r matrix factorization algorithm combining with similarity decaying is proposed. And it takes time information into the similarity calculation. Through the collaborative filtering algorithm based on time information user-user similarity and item-item similarity are calculated. These similarities values are set as the initial values of error function. Then matrix factorization is used to calculate user-user and item-item similarities,which is set as predicted values. Finally we use the difference between the initial value and predictive value to construct the error function. In order to minimize the error function,a stochastic gradient descent method is used to train the model iteratively. Experimental results based on Movie Lens showthat the recommendation algorithm can improve the recommendation accuracy.