## 4 Numerical Experiments
### Experimental Results
#### 4.2.2 Eachmovie Dataset
Although the RF R-square-based score is a weighted average of the RF item modeling-based prediction and the RF user modeling-based prediction, the first, second, third, and seventh observations violate the assumption that the weighted mean should fall between the predicted value of the RF item modeling and the predicted value of the RF user modeling, as illustrated in Figure 3, because the averages of the R-square values have negative signs. As a result, the RF R-square-based score does not work well. Instead, we apply the Pearson correlation-based score to the RF item modeling and the RF user modeling. For Top-1, Top-3, Top-4, and Top-10, the RF Pearson correlation-based score performs the best and is close to the item modeling for the other Top-\(N\) accuracies, as shown in Table 6. Moreover, the RF Pearson correlation-based score gives the best average of the ten Top-\(N\) accuracies. Thus, the RF Pearson correlation-based score works better for the two-way cooperative CF than the RF R-square-based score. To understand these matters better, we randomly select 10 test data and calculate predicted values for the RF user modeling, the RF item modeling, and the RF Pearson correlation-based score (Figure 4), where 1 denotes a response and \(-1\) denotes a non-response. The RF Pearson correlation-based score should be a weighted average of the RF item modeling-based \begin{table}
\begin{tabular}{l|l l l l|l l l|l l l l} \hline \hline  & **PCA** & **PCA** & **PCA** & **PCA** & **PCA** & & & & & & & & & RF \\ \(N\) & **+LR** & **+LR** & **+LR** & **+LR** & **Pearson** & **Pearson** & **RF** & **RF** & **RF** & **RF** & **Pearson** \\  & **User** & **Item** & **2-Way 1** & **2-Way 2** & **User** & **Item** & **Score** & **User** & **Item** & **2-Way** & **Score** \\ \hline
1 & 0.76 & **0.87** & NA & 0.69 & 0.84 & 0.68 & **0.85** & 0.86 & **0.88** & 0.70 & **0.88** \\
2 & 0.73 & **0.87** & NA & 0.74 & **0.84** & 0.63 & 0.83 & 0.84 & **0.86** & 0.71 & 0.85 \\
3 & 0.71 & **0.85** & NA & 0.74 & **0.82** & 0.62 & 0.82 & 0.83 & 0.84 & 0.73 & **0.85** \\
4 & 0.67 & **0.84** & NA & 0.74 & **0.81** & 0.62 & 0.80 & 0.81 & 0.81 & 0.70 & **0.83** \\
5 & 0.64 & **0.82** & NA & 0.71 & **0.77** & 0.62 & 0.77 & 0.76 & **0.79** & 0.67 & 0.79 \\
6 & 0.61 & **0.78** & NA & 0.69 & **0.75** & 0.61 & 0.74 & 0.74 & **0.76** & 0.65 & 0.75 \\
7 & 0.59 & **0.75** & NA & 0.67 & **0.71** & 0.59 & 0.71 & 0.70 & **0.73** & 0.64 & 0.73 \\
8 & 0.57 & **0.71** & NA & 0.64 & 0.68 & 0.57 & **0.68** & 0.68 & **0.70** & 0.63 & 0.70 \\
9 & 0.56 & **0.69** & NA & 0.62 & **0.66** & 0.56 & 0.66 & 0.65 & **0.68** & 0.60 & 0.68 \\
10 & 0.55 & **0.67** & NA & 0.61 & **0.64** & 0.54 & 0.64 & 0.63 & **0.65** & 0.59 & **0.65** \\ \hline Avg. & 0.64 & **0.79** & NA & 0.69 & **0.75** & 0.60 & 0.75 & 0.75 & 0.77 & 0.66 & **0.77** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Top-\(N\) accuracy for case 4. Figure 3: Predicted values for the RF R-square-based score. prediction and the RF user modeling-based prediction. In this case, no observations violate the assumption. In other words, the RF Pearson correlation-based scores always fall between the predicted value of the RF item modeling and the RF predicted value of the user modeling. Thus, the RF Pearson correlation-based score works more effectively than the RF R-square-based score for the two-way cooperative CF. Additionally, although the proposed CF scheme for the RF R-square-based score in Section 3 \(D\) requires more procedures, it improves the prediction performance of the RF R-square-based score dramatically, as shown in Table 6. As illustrated in Figure 5, the proposed CF scheme emulates the RF Pearson correlation-based score. Indeed, the average of the ten Top-\(N\) accuracies for the proposed CF scheme, 0.7737, is greater than that of the ten Top-\(N\) accuracies for the Pearson correlation-based score, 0.7696. We realize that the proposed CF scheme performs as well as the RF Pearson correlation-based score for the two-way cooperative CF.