## 3 Proposed Method
### Performance Comparison  
Tables 1 and 2 show the performance of each TV recommendation method in terms of HR and AR as the size of recommendation list, \(K\), changes from 1 to 5. The methods are divided into three groups, which are CF methods, popular item-based methods, and QP-based methods.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **K = 1** & **K = 2** & **K = 3** & **K = 4** & **K = 5** \\ \hline kNN & 24.31 & 41.59 & 53.16 & 60.15 & 65.73 \\ SVD & 25.93 & 39.31 & 48.20 & 54.69 & 59.49 \\ Pop\_usual & 29.51 & 51.08 & 67.09 & 75.89 & 80.79 \\ Pop\_day & 30.30 & 51.15 & 65.84 & 74.14 & 79.15 \\ Pop\_hour & 33.20 & 53.93 & 67.78 & 75.68 & 80.19 \\ Pop\_dayhour & 34.02 & 52.61 & 64.83 & 73.57 & 78.38 \\ QP\_log & 35.49 & 55.41 & 69.04 & 76.87 & 81.41 \\ Proposed & 37.31 & 56.91 & 69.90 & 76.56 & 80.35 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Hit rate of TV recommender systems (%).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Method** & **K = 1** & **K = 2** & **K = 3** & **K = 4** & **K = 5** \\ \hline kNN & 1.00 & 1.30 & 1.62 & 1.87 & 2.09 \\ SVD & 1.00 & 1.24 & 1.53 & 1.79 & 2.02 \\ Pop\_usual & 1.00 & 1.43 & 1.81 & 2.07 & 2.26 \\ Pop\_day & 1.00 & 1.41 & 1.77 & 2.03 & 2.24 \\ Pop\_hour & 1.00 & 1.39 & 1.73 & 1.97 & 2.15 \\ Pop\_dayhour & 1.00 & 1.36 & 1.68 & 1.96 & 2.16 \\ QP\_log & 1.00 & 1.37 & 1.69 & 1.94 & 2.12 \\ Proposed & 1.00 & 1.35 & 1.66 & 1.88 & 2.03 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Average rank of TV recommender systems.  
In CF methods, \(kNN\) was generally better than \(SVD\) in terms of HR. In popular based methods, _Pop_hour_ and _Pop_dayhour_, which considered more detailed time context, were better than others when \(K\) was small. Otherwise, when \(K\) was large, _Pop_dayhour_ was worse than others. All QP-based methods outperformed other methods. This implied that multi-time contextual profiling was more effective to increase the quality of the system than using only a detailed time context such as _Pop_dayhour_.  
When comparing with _QP_log_, the overall performance of the proposed method was prominent, though it had fewer constraints. In terms of AR, the proposed method outperformed _QP_log_ for any value of \(K\). The improvement of AR was increasing as \(K\) became large. When \(K\) was 1-3, the proposed method improved AR by 1-2%, but, when \(K\) was 4-5, it improved by 3-4%. In terms of HR, the proposed method was better when \(K\) was 1-3 and was slightly lower when \(K\) became large. When \(K\) was 1-3, the improvement was around 1-5%, but around \(-1\%\) when \(K\) was 4-5. Even though HR slightly decreased when \(K\) was large, the improvement of AR, which was about 4%, could compensate for it. Thus, we could conclude that the proposed method more accurately recommends TV programs than the other approaches. Interestingly, the proposed methods showed the maximum improvement of HR when \(K=1\). It improved by 5-50% compared to the baselines. This means that the proposed method very effectively pinpoints TV programs that the target user will watch.  
Also, the proposed method was more practical because it required very little computing cost. Figure 2 shows the optimization time of _QP_log_ and the proposed method as the size of watching logs increases. Since _QP_log_ is based on records in watching history, the optimization time very rapidly increased as the number of records increases. However, the optimization time of the proposed method was bounded by a constant as mentioned in Section 3. If there are some day-hour time slots in which the target user did not watch TV, we could remove constraints for the time slots. So, the actual optimization time was lower than an upper bound as shown in Figure 2. It proves that the proposed method is scalable.