## 2 Background and Related Work
### Time-Aware Recommender Systems
#### 2.2.1 Evolution of User Preferences
The methods described above can be considered as the background approaches for dealing with the evolution of preferences; however, other proposals have been reported in the literature. Some methods can be placed in some of the established groups of techniques, but others are hybrid approaches that include characteristics of more than one category. Some representative papers are analyzed below. [PERSON] presented in [43] a method for recommending lecture materials, in which the time similarity between items is computed considering their download dates and the recommendation time \(t\). The similarity metric for two items \(i\) and \(j\) is defined in Equation (10), in which the second addend in the denominator is introduced to penalize the less recent ratings. \[S_{ij}(t)=\frac{1}{\left|t_{i}-t_{j}\right|+\left|\min\!\left(t_{i},t_{j}\right) -t\right|} \tag{10}\]  
This proposal is a recency approach designed for item-based CF. Similar to the problem at hand in this paper, no explicit ratings are needed, since the downloading of materials is used as implicit user feedback. However, the extension of this approach to the field of music would be complicated due to the fact that a certain material is usually downloaded only once by a given user, while a song is usually played multiple times by the same person. A recency-based method is also proposed in [44], where the interest drift over time is captured by means of a linear function. This function needs to be computed for the different time bins into which the full time period under consideration is divided. This proposal has been designed for the specific scenario of one-class collaborative filtering, which takes place when only positive (e.g., like) or unknown user-item feedback is available. Often, missing values are related to not-liked items, but this is not always true. Aiming at avoiding this problem, a variant of the LDA (latent dirichlet allocation) model is used for capturing latent topics from the user-item rating matrix and identifying users' latent interests. Although LDA is usually used in the text processing area, in the context of this work, documents are replaced by users and words by items. This method is only applicable when timestamped explicit feedback is available. In addition, time intervals must be created, unlike our approach, in which it is not necessary. In [45], the preference changes over time are addressed by identifying overlapping communities among users from a time-weighted user similarity matrix. To create this matrix, timestamped ratings or transactions are used to split the dataset into several subsets for different time periods. When computing the similarity between users, these time intervals are taken into account since it is expected that the similarity is greater when they have common items rated in the same period. The main objective of grouping similar users into overlapping clusters is to overcome sparsity and cold-start problems. Recommendations are based on a model of association rules that are mined from each community. The data involved in these rules are binary ratings relating users and items, that is, the information about items that have been rated or purchased by the corresponding users. Subsets corresponding to different time partitions are needed again to introduce time effects, and a time-based confidence measure is defined to determine which are the best rules for making recommendations. The proposal is validated with two movie datasets. Although transactions can be used as implicit feedback in this work, only binary values are managed (whether an item has been purchased/rated or not) for both implicit and explicit ratings. Our objective is to work with multivalued ratings since they provide more information. Regarding temporal factor models for capturing trends, one of the most known methods is time-SVD++ [46], which introduces a modification in the original SVD++ matrix factorization method.