Abstract: With the advent of social networks, trust-aware recommendation methods have been well studied. Most of these algorithms assume that trusted users will have similar tastes. However, this assumption ignores the fact that two users may establish a trust connection for the social purpose or simply for etiquette, which may not result in similar opinions on the same item. Motivated by this observation, a novel trust strength aware social recommendation method, StrengthMF, is firstly proposed. Compared with previous methods, this new approach assumes that a trust relation does not necessarily guarantee the similarity in preferences between two users. Specificly, StrengthMF learns the trust strength and distinguishes users with more similar interests through the shared user latent feature space, i.e., the user latent feature space in trust network is the same in the rating matrix. This will allow us to acquire a better understanding of the relationship between trust relation and rating similarity. To validate the learned trust strength, InfluenceMF method is then proposed, which retrains SocialMF with estimated trust relations. Experimental results on real world product rating data set Epinions show that the proposed approaches outperform the state-of-the-art algorithms in terms of RMSE and MAE, and the learned trust strength can further improve traditional recommendation methods.