In many application domains of recommender systems, explicit rating information is sparse or non-existent. The preferences of the current user have therefore to be approximated by interpreting his or her behavior, i.e., the implicit user feedback. In the literature, a number of algorithm proposals have been made that rely solely on such implicit feedback, among them Bayesian Personalized Ranking (BPR). In the BPR approach, pairwise comparisons between the items are made in the training phase and an item i is considered to be preferred over item j if the user interacted in some form with i but not with j. In real-world applications, however, implicit feedback is not necessarily limited to such binary decisions as there are, e.g., different types of user actions like item views, cart or purchase actions and there can exist several actions for an item over time. In this paper we show how BPR can be extended to deal with such more fine-granular, graded preference relations. An empirical analysis shows that this extension can help to measurably increase the predictive accuracy of BPR on realistic e-commerce datasets.
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