The advent of social networks and activity networks affords us an opportunity of utilizing explicit social information and activity information to improve the quality of recommendation in the presence of data sparsity. In this article, we present a social-influence-based collaborative filtering (SICF) framework over heterogeneous information networks with three unique features. First, we integrate different types of entities, links, attributes, and activities from rating networks, social networks, and activity networks into a unified social-influence-based collaborative filtering model through the intra-network and inter-network social influence. Second, we propose three social-influence propagation models to capture three kinds of information propagation within heterogeneous information networks: user-based influence propagation on user rating networks, item-based influence propagation on user-rating activity networks, and term-based influence propagation on user-review activity networks, respectively. We compute three kinds of social-influence-based user similarity scores based on three social-influence propagation models, respectively. Third, a unified social-influence-based CF prediction model is proposed to infer rating tastes by incorporating three kinds of social-influence-based similarity measures with different weighting factors. We design a weight-learning algorithm, SICF, to refine the prediction result by quantifying the contribution of each kind of information propagation to make a good balance between prediction accuracy and data sparsity. Extensive evaluation on real datasets demonstrates that SICF outperforms existing representative collaborative filtering methods.