Abstract: Social trust aware recommender systems have been well studied in recent years. However, most of existing methods focus on the recommendation scenarios where users can provide explicit feedback to items. But in most cases, the feedback is not explicit but implicit. Moreover, most of trust aware methods assume the trust relationships among users are single and homogeneous, whereas trust as a social concept is intrinsically multi-faceted and heterogeneous. Simply exploiting the raw values of trust relations cannot get satisfactory results. Based on the above observations, we propose to learn a trust aware personalized ranking method with multi-faceted trust relations for implicit feedback. Specifically, we first introduce the social trust assumption——a user's taste is close to the neighbors he/she trusts——into the Bayesian Personalized Ranking model. To explore the impact of users' multi-faceted trust relations, we further propose a categorysensitive random walk method CRWR to infer the true trust value on each trust link. Finally, we arrive at our trust strength aware item recommendation method SocialBPRCRWR by replacing the raw binary trust matrix with the derived real-valued trust strength. Data analysis and experimental results on two real-world datasets demonstrate the existence of social trust influence and the effectiveness of our social based ranking method SocialBPRCRWR in terms of AUC (area under the receiver operating characteristic curve).