Pearson相关系数下非对称相似度计算及其应用

Asymmetric similarity calculation and application under pearson correlation coefficient

稀疏性是推荐算法存在的问题之一,解决稀疏性问题的常用方法是矩阵分解,矩阵分解结合用户相似度可以提高推荐的准确率,但是传统的相似度计算方法并未考虑用户对项目评分数量的差异,因此构建的相似度矩阵是对称的.针对这一问题,结合Pearson相关系数,给出一种新的计算方法——用户非对称相似度.在考虑用户对相同项目评分的同时,计算用户间评分相同的项目数与用户所有评分项目数的比值,以此拉近用户之间相似的程度,且得到用户之间的非对称关系.其次,利用用户非对称相似度方法计算用户间相似度矩阵,将相似度矩阵与用户评分矩阵融入到概率矩阵分解框架中,实现用户的社会化推荐.在公开数据集上测试,结果显示改进的非对称相似度公式相比传统的相似度计算公式,在稀疏的数据集上进行社会化推荐能得到更准确的推荐结果.

Sparsity is one of the problems of recommendation algorithms.The existing method to solve the problem of sparsity is the matrix factorization.The matrix factorization combined with user similarity can improve the accuracy of recommendation.However,the traditional similarity calculation method does not consider the difference in the number of items scored by users,so the constructed similarity matrix is symmetric.In response to this problem,a new calculation method called user asymmetric similarity is proposed by combining Pearson correlation coefficient.While considering users ratings of the same item,calculate the ratio of the number of items with the same rating among users to the number of all scoring items of users,so as to describe the similarity between two users,and get the asymmetric relation between users.Secondly,use the user asymmetric similarity method to calculate the similarity matrix between users,and the similarity matrix and user rating matrix are integrated into the probability matrix factorization framework to achieve the social recommendation of users.Tested on public datasets,the results showed that the improved asymmetric similarity formula,compared to the traditional similarity calculation methods,can achieve more accurate recommendation results through socialized recommendations on sparse datasets.