## 2 Background and Related Work
### Time-Aware Recommender Systems
#### 2.2.2 Temporal Context  
In context-aware systems, contextual dimensions are added to the item and user dimensions involved in traditional CF models. Then, traditional 2D models are replaced by 3D models with the aim to adapt recommendations to the specific context of the user, since preferences of users for a given item can change depending on contextual variables. In the case of time-aware recommender systems, time is the contextual dimension, which is modeled as a discrete variable representing the context (time of day, day of the week, season, etc.). Three strategies can be applied in order to make recommendations for specific contexts: contextual pre-filtering, contextual post-filtering and contextual modeling. Pre-filtering methods apply 2D CF, but only use the ratings associated with the target context. For instance, in order to recommend movies to watch at the weekend, only the ratings of movies watched on weekend are used. Contextual post-filtering methods initially ignore contextual information and recommendations are obtained using traditional 2D approaches. Then, several procedures can be used to select some items to be recommended in the target context or to adjust the ranking of these items, making use of contextual information. In contextual modeling, a 3D model incorporating contextual information is used to make recommendations. One way to do this is to compute the similarity between users or items, not only taking into account the ratings, but also contextual factors such as time. One of the main drawbacks of pre-filtering methods is the sparsity, which is caused by the fact that ratings irrelevant to a given target context are removed. Additionally, post-filtering methods usually require the use of content information to provide contextual recommendations. For example, if a movie genre or the movies of a specific actor/director are often watched on the weekends, this content information (genre, actor, etc.) is used to adjust recommendations to the context of the user [18]. There are many studies where time is used as a contextual variable in many domains. The time of the year is considered in a comparative study of pre- and post-filtering approaches [58] conducted using a dataset of electronic products that are sold through an e-commerce system. A user-based CF method is applied to compare the results of both techniques. Categories of products are used instead of individual items, and implicit ratings are computed from the frequencies of purchases. The authors conclude that, although the results depend on the specific method of each filtering type, good post-filtering approaches should be better than pre-filtering. Time-aware recommender systems have also been developed in the field of services to help users discover the most suitable ones [59]. Recommendations are based on historical service quality (QoS) data that are usually distributed and owned by different companies, who are unable to make this information public so as to protect user privacy. In [59], the locality-sensitive hashing (LSH) technique has been modified by incorporating slots referring to the time when users invoke the services. LSH was introduced into service recommendations as a means to integrate multi-source data while preserving privacy. Time combined with additional contextual factors has been widely studied. For example, the place, time and company are the contextual variables involved in the film recommendation system presented in [60]. In this work, a multidimensional approach is proposed to jointly manage information regarding users, items and contextual information. The ratings are estimated using a reduction-based approach that applies the classical CF technique on contextual segments. In recent years, the improvement of recommendations through the exploitation of contextual information has been the focus of intensive research [61]. The possibility of obtaining this information through mobile devices has led to the development of context-aware recommendation systems in many application domains.