## 3 Modeling the Time Effect on Music Recommendations
### Time-Aware Music Recommendation Method
#### 3.2.1 Modeling the Evolution of Preferences
This is because the MAE and RMSE errors are lower with the ratings



to changes that do not affect the first items on the list. These small differences also mean that the proportion of relevant items in the lists, as well as in the top-5, top-10 and top-15 positions, remain almost unchanged. As a result, the differences in the values of all rank-based metrics for ratings and decay ratings are in non-significant digits, even though the overall error rate was lower for the decay ratings. Figure 9 shows that most of the metrics were significantly improved by introducing the time of day attribute when using the proposed user-time K-NN method for both the complete day and the morning and evening intervals. The AUC and NDCG values are significantly higher in all cases for both the ratings and decay ratings. The metrics, prec@5, prec@10, prec@15 and MAP, also present much higher values during the evening intervals, which is not always the case for the complete day and the morning intervals. The results are therefore not as good for the top-N lists as they are for the rating prediction. This can also be explained by the reasons given before, which are related to the effect on the rank-based metrics of the closeness of the implicit evaluation values for the relevant songs, as well as the large number of songs contained within the dataset. ## 5 Conclusions

One of the most influential factors in music recommendation is time. Moreover, its influence can depend on various aspects such as the evolution of user preferences and the time when users listen to songs. These aspects have been studied in-depth, but as far as we know, the evolution of preferences has never been modeled directly from implicit feedback. In addition, time has also been considered as a contextual variable in other studies in order to make recommendations based on the time of day, but it is not used to characterize users according to their listening habits. In this paper, an approach is proposed to address the effects of time on music recommendations. The method is designed to deal with problems characteristic of the music field which are absent in other application domains. The study also attempts to manage implicit feedback, since explicit ratings are not usually available. Thus, the evolution of user preferences over time is included in the proposed method for obtaining the implicit ratings of songs from the frequency of plays. Other commonly used methods for incorporating time dynamics, such as decay functions, cannot be used here because they require timestamped explicit ratings. Likewise, the traditional way of computing implicit ratings, such as using the time users spend on examining an item or the purchase information, are not applicable in the music domain. This occurs because users tend to listen to a song more than once and the songs are not bought one by one on the streaming platforms. Furthermore, the proposed recommender model incorporates information from the listening behavior of users in order to improve recommendations. The results of the validation performed using a dataset from Last.fm proved that the proposed method for recommending songs outperforms other collaborative filtering approaches, when the context of time is or is not taken into account. Conceptualization, M.N.M.-G. and Y.Z. ; methodology, D.S.-M., M.N.M.-G. and Y.Z. ; software, D.S.-M.; validation, D.S.-M. and M.N.M.-G.; data curation, D.S.-M.; supervision, Y.Z. and M.N.M.-G.; funding acquisition, M.N.M.-G. All authors have read and agreed to the published version of the manuscript. This research was funded by the Junta de Castilla y Leon, Spain, grant number: SA064G19. The authors declare no conflict of interest

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