## 3 Modeling the Time Effect on Music Recommendations
### Time-Aware Music Recommendation Method
#### 3.2.1 Modeling the Evolution of Preferences
Other methods for modeling the evolution of user preferences cannot be applied since they need timestamped ratings, as explained in detail in Section 3. The methods applied for providing top-N recommendations were the user K-NN, weighted regularized matrix factorization (WRMF) [32; 81] and Bayesian personalized ranking matrix factorization (BPRMF) [31]. ### Modeling Temporal Evolution of Preferences

#### 4.3.1 Rating Prediction

The first experiments were carried out without considering the context of time. Thus, the entire dataset of song listening information taken within a 24-h period was used. We compared the outcome of several recommender methods using implicit ratings, computed following the method proposed by [PERSON], in two ways, without considering temporal effects (ratings), and considering those effects by applying our proposed method (decay ratings). The decay ratings were computed using Equations (11-13). The optimal value of \(\lambda\) in Equation (11) was set to 0.4 after some preliminary tests proved that this value yields the lowest error rates. The first results shown in Table 1 correspond to the rating prediction for the complete day when the time effect was not considered in the generation of implicit ratings (ratings) and when it was taken into account according to our proposal (decay ratings). We can observe that a significant reduction in the rate of errors (columns \"improv.\") was achieved when using decay ratings against the ratings of all recommendation methods. The MAE was reduced by 8.1-22.5%. The next step was to validate the method when considering the context of the time of day. To do so, the dataset was divided into time intervals according to the proposal of [61], where time intervals were established for the morning and evening hours. Morning was defined as the hours between 5 am and 6 pm and evening as the remaining hours of the day. [PERSON] and [PERSON] [61] study the time partition that provides the lowest error rates using a Last.fm dataset for artist recommendations. However, our aim is not to prove that the context of time can improve recommendations, but to prove that the improvements of our approach (using decay ratings instead of ratings), achieved without considering the time context, are extensible to contextual time intervals. [PERSON] and [PERSON] report an improvement of 2.4% in the MAE associated with recommendations for the morning and evening time frames as opposed to the complete 24-h period. The dataset was extracted from Last.fm and used to recommend artists to users by means of the CF method. A five-fold cross validation was applied in the experiments. In a preliminary study, we applied the same method and the same validation procedure to our dataset, in this case for recommending songs. However, instead of decreasing, the values for the MAE for the morning and evening periods slightly increased, when compared to the complete 24-h period. Following on, we proceeded to check the behavior when using the previously described training and test set partition, in which examples of the test set correspond to the dates subsequent to those of the training set examples. Table 1 also presents the results obtained in the experiments involving the two time periods (morning and evening). An analysis of the values showed that the most significant result is that the error rates for the morning and evening periods were substantially lower than those of the complete time period (day) when traditional ratings were used. However, this reduction was less obvious when