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Over the past two decades, a large amount of research effort has been devoted to developing algorithms that generate recommendations. The resulting research progress has established the importance of the user-item (U-I) matrix, which encodes the individual preferences of users for items in a collection, for recommender systems. The U-I matrix provides the basis for collaborative filtering (CF) techniques, the dominant framework for recommender systems. Currently, new recommendation scenarios are emerging that offer promising new information that goes beyond the U-I matrix. This information can be divided into two categories related to its source: rich side information concerning users and items, and interaction information associated with the interplay of users and items. In this survey, we summarize and analyze recommendation scenarios involving information sources and the CF algorithms that have been recently developed to address them. We provide a comprehensive introduction to a large body of research, more than 200 key references, with the aim of supporting the further development of recommender systems exploiting information beyond the U-I matrix. On the basis of this material, we identify and discuss what we see as the central challenges lying ahead for recommender system technology, both in terms of extensions of existing techniques as well as of the integration of techniques and technologies drawn from other research areas.

Pairwise learning-to-rank algorithms have been shown to allow recommender systems to leverage unary user feedback. We propose Multi-feedback Bayesian Personalized Ranking (MF-BPR), a pairwise method that exploits different types of feedback with an extended sampling method. The feedback types are drawn from different "channels", in which users interact with items (e.g., clicks, likes, listens, follows, and purchases). We build on the insight that different kinds of feedback, e.g., a click versus a like, reflect different levels of commitment or preference. Our approach differs from previous work in that it exploits multiple sources of feedback simultaneously during the training process. The novelty of MF-BPR is an extended sampling method that equates feedback sources with "levels" that reflect the expected contribution of the signal. We demonstrate the effectiveness of our approach with a series of experiments carried out on three datasets containing multiple types of feedback. Our experimental results demonstrate that with a right sampling method, MF-BPR outperforms BPR in terms of accuracy. We find that the advantage of MF-BPR lies in its ability to leverage level information when sampling negative items.

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