## 3 Modeling the Time Effect on Music Recommendations
### Time-Aware Music Recommendation Method
#### 3.2.1 Modeling the Evolution of Preferences
Only the outcome of the WRMF method with ratings and decay ratings is presented, since the user K-NN produced worse results and did not give appreciable differences between the ratings and decay ratings. The results of the metrics the AUC, NDCG and MAP do not reveal a clear improved performance when the morning and evening time periods are considered, compared to the complete day. The NDCG value is always lower for the morning and evening time periods, while the AUC and MAP values are higher for the evening period when using both the ratings and decay ratings. However, for the morning period, the AUC was higher only when using ratings, and the MAP was lower for ratings and decay ratings when compared to the complete day. Regarding prec@5, prec@10, prec@15, the behavior is irregular, similar to what is observed for the rating prediction. In general, it can be seen that all the precision values are low, regardless of the time period, the type of ratings and the recommendation method. This fact is compatible with the reasoning given at the beginning of Section 4 regarding the method used to generate the top-N lists, which is suitable for comparison between methods but not for evaluating the performance in absolute terms. The high number of songs in the dataset aggravates this problem. ### Modeling Listening Habits of Users

In the second part of the work, we studied the frequency of plays throughout the day to detect the listening behavior of users in relation to time. We analyzed the play frequencies for all users as a complete group (Figure 4), as well as for each individual user (Figures 5 and 6). Figure 4 shows the distribution of the frequency values during the morning intervals and the distribution of values during the evening intervals, according to the partition mentioned in the previous section. Therefore, this figure shows the listening pattern of all users in the dataset over the day, from 0 to 24 h. We can observe that the maximum frequency was reached around 6 p.m. The figure also shows that morning frequencies present some fluctuations, while the evening frequencies gradually decay during 6 pm to 5 am. When time intervals are established to make context-aware recommendations, this overall pattern is exploited. However, in order to achieve a greater degree of personalization, it is necessary to take into account the individual patterns of each user. When the play frequencies were analyzed individually, different distributions could be found for the various users, since their listening habits were not the same. Figures 5 and 6 present a sample of users exhibiting different behaviors for both the evening and morning intervals. We can see there was

Figure 3: Values of the top-N metrics given by WRMF using the ratings and decay ratings for different day time periods. greater variability during the morning period than in the evening, at which time the distributions were more similar. Figure 4: Day time frequencies of plays during the morning intervals and the evening intervals. Figure 5: Individual day time frequencies of plays for different users during the evening intervals. Based on this analysis, we propose to use the time listening behavior to characterize the users and to incorporate this behavior in the recommender models as a means to improve the reliability of the recommendations. The average time of day for each user \(u_{i}\) was used to introduce the listening habits in the recommendation model, which was managed as an additional attribute that allows the similarity to be detected between users in collaborative filtering. The incorporation of this variable into collaborative filtering was tested for both the rating prediction and top-N recommendations. The method used was the K-nearest neighbor (K-NN) user-based collaborative filtering, which is called \"user attribute K-NN\" and is when other attributes besides the ratings are used to compute the similarity between users. In this case, the metric used is the cosine-similarity.