## 3 Modeling the Time Effect on Music Recommendations
### Time-Aware Music Recommendation Method
#### 3.2.1 Modeling the Evolution of Preferences
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**MAE**} & \multicolumn{2}{c}{**RMSE**} & \multicolumn{2}{c}{**NMAE**} \\ \hline \multirow{6}{*}{Day (24 h.)} & \multirow{2}{*}{**Ratings**} & \multicolumn{2}{c}{**Decay**} & \multirow{2}{*}{**Improv.**} & \multirow{2}{*}{**Ratings**} & \multicolumn{2}{c}{**Decay**} & \multirow{2}{*}{**Improv.**} & \multirow{2}{*}{**Ratings**} & \multicolumn{2}{c}{**Decay**} \\  & & & **Ratings** & & & & & & Ratings \\ \cline{1-1}  & K-NN Pearson & 1.265 & **1.037** & **18.02\%** & 1.570 & **1.299** & **17.26\%** & 0.316 & **0.259** \\  & K-NN Cosine & 1.303 & **1.066** & **18.19\%** & 1.601 & **1.340** & **16.30\%** & 0.326 & **0.267** \\  & MF & 1.263 & **1.028** & **18.61\%** & 1.569 & **1.291** & **17.72\%** & 0.316 & **0.257** \\  & BMF & 1.229 & **0.952** & **22.54\%** & 1.529 & **1.179** & **22.89\%** & 0.307 & **0.238** \\  & FWMF & 1.279 & **1.176** & **8.05\%** & 1.582 & **1.499** & **5.25\%** & 0.320 & **0.294** \\ \hline \multirow{6}{*}{Morning} & K-NN Pearson & 1.048 & **1.006** & **4.01\%** & 1.310 & **1.273** & **2.82\%** & 0.262 & **0.251** \\  & K-NN Cosine & 1.090 & **1.060** & **2.75\%** & 1.353 & **1.345** & **0.59\%** & 0.273 & **0.265** \\  & MF & 1.025 & **0.948** & **7.51\%** & 1.260 & **1.186** & **5.87\%** & 0.256 & **0.237** \\  & BMF & 1.008 & **0.919** & **8.83\%** & 1.240 & **1.147** & **7.50\%** & 0.252 & **0.230** \\  & FWMF & 1.055 & **1.004** & **4.83\%** & 1.294 & **1.271** & **1.78\%** & 0.264 & **0.251** \\ \hline \multirow{6}{*}{Evening} & K-NN Pearson & 1.094 & **1.023** & **6.49\%** & 1.370 & **1.293** & **5.62\%** & 0.274 & **0.256** \\  & K-NN Cosine & 1.100 & **1.088** & **1.09\%** & 1.389 & **1.371** & **1.30\%** & 0.275 & **0.272** \\ \cline{1-1}  & MF & 1.047 & **0.978** & **6.59\%** & 1.317 & **1.232** & **6.45\%** & 0.262 & **0.245** \\ \cline{1-1}  & BMF & 1.034 & **0.946** & **8.51\%** & 1.294 & **1.183** & **8.58\%** & 0.258 & **0.237** \\ \cline{1-1}  & FWMF & 1.196 & **1.097** & **8.28\%** & 1.527 & **1.399** & **8.38\%** & 0.256 & **0.227** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The root-mean-square error (RMSE), mean absolute error (MAE) and normalized mean absolute error (NMAE) values obtained for the rating prediction when contextual information is not considered (day) and when contextual pre-filtering is carried out (morning and evening). the decay ratings were used. For the ratings, the MAE decreases between 16.3% and 18.8% when comparing the morning period with the complete day, and between 6.5% and 17.1% when comparing the evening with the complete day. For the decay ratings, the reduction in the MAE varied between 0.6% and 14.6% when comparing the morning period with the complete day and between 0.6% and 6.7% when comparing the evening with the complete day. In the latter case, an increment of 2.1% was produced for K-NN with the cosine similarity, which was the method that yielded the worst results in all the experiments. Another conclusion that can be drawn from this analysis is that the decay ratings provided the best results for all methods tested in this study. Although, for the morning and evening periods, the improvement was not as great as the one achieved for the complete day, where the reduction in the MAE varied between 1.1% and 11.3%. Figure 1 shows a comparison of the results obtained in these experiments, where it can be seen that the error rates (MAE and RMSE) are lower for the decay ratings as compared to the ratings, obtaining the longest distance for the complete day. The best values for each method and the percentages of improvement are highlighted in bold. Finally, to confirm that the method can be applied in the col-start scenario, as stated in the description of the proposal, we have conducted some additional experiments. From the entire dataset, the five most recent users have been selected since they have a much shorter play history than the oldest users.