Abstract: Research suggests that adding explicit social trust to social network recommendations significantly improves the predictive accuracy of the scoring, but it is difficult to get trust score of users in real life. Previously, some scholars have studied and proposed a trust measurement method to calculate and predict the interaction between users and trust score. In this paper, a method of social trust relationship extraction based on Hellinger distance is proposed, and the similarity calculation is carried out by describing the f-divergence of one side node in binary network. Then, a new probability matrix factorization algorithm（CH-PMF） based on user group and implicit social relation is proposed by adding the hidden information to the improved probability matrix. Experimental results show that the proposed model has almost the same performance as the actual result of the actual trust score expressed by users, and CH-PMF has a better recommendation than other traditional algorithms when the trust data can not be extracted.

Key words: social network, recommendation system, probability matrix factorization, trust relationship

摘要： 研究表明在社会网络推荐中添加明确的社会信任明显提高了评分的预测精度，但现实生活中很难得到用户之间明确的信任评分。之前已有学者研究并提出了信任度量方法来计算和预测用户之间的相互作用及信任评分。提出了一种基于Hellinger距离的社会信任关系提取方法，通过描述二分网络中一侧节点的f散度来进行用户相似度计算。然后结合用户分组信息，将提取的隐式社会关系加入改进的概率矩阵分解中，提出一种新的基于用户组群和隐性社会关系的概率矩阵分解算法（CH-PMF）。实验结果表明，提出的模型与应用实际用户明确表示的信任分数推荐结果表现几乎相同，且在无法提取到明确信任数据时，CH-PMF有着比其他传统算法更好的推荐效果。

关键词: 社会网络, 推荐系统, 概率矩阵分解, 信任关系