## 4 Numerical Experiments
### Experimental Results
#### 4.2.2 Eachmovie Dataset
Then, the calculated weighted average based on (9) is \(-1.215328\), which does not make sense because it does not fall between \(-0.3204994\) and \(0.5009333\). Therefore, the RF R-square-based score does not work well in this case. Instead of the RF R-square-based score, we apply the Pearson correlation-based score to the RF item and user modeling. For Top-_1_ and Top-_4_ to Top-_6_, the RF Pearson correlation-based score performs the best and is close to the RF user modeling or the RF item modeling for the other Top-_N_ accuracies. Moreover, the RF Pearson correlation-based score gives the best average of the ten Top-_N_ accuracies. As a result, we realize that the RF Pearson correlation-based score works better for the two-way cooperative CF than the RF R-square-based score. For case 4, as shown in Table 6, the PCA+LR item modeling performs better than the other approaches for all the Top-_N_ accuracies. The PCA+LR two-way 2 does not seem to outperform the PCA+LR item modeling, although it clearly outperforms the PCA+LR two-way 1. The PCA+LR two-way 1 does not even provide appropriate predicted values. For the user-based CF and item-based CF, the user-based CF and the Pearson correlation-based score outperform the item-based CF for all the Top-_N_ accuracies. The Pearson correlation-based score does not seem to perform the best, except for Top-_1_ and Top-_8_. The RF R-square-based score is outperformed by the RF user modeling and the RF item modeling. Note that there are only 20 items in section A\(\times\) C in Figure 1a. In this case, the rows of some active users in the binary market basket data are all zeros, which is the extreme high-dimensional cold-start problem. Then, the average of the R-square values can have a negative sign, which can lead to bad prediction performance. \begin{table}
\begin{tabular}{l|l l l l|l l l|l l l l} \hline \hline \multirow{2}{*}{**N**} & \multicolumn{2}{c}{**PCA+LR**} & \multicolumn{2}{c}{**PCA+LR**} & \multicolumn{2}{c}{**PCA+LR**} & \multicolumn{2}{c}{**PCA+LR**} & \multicolumn{2}{c}{**Pearson**} & \multicolumn{2}{c}{**Pearson**} & \multicolumn{2}{c}{**Pearson**} & \multicolumn{2}{c}{**RF**} & \multicolumn{2}{c}{**RF**} & \multicolumn{2}{c}{**RF**} \\  & **User** & **Item** & **2-Way 1** & **2-Way 2** & **User** & **Item** & **Score** & **User** & **Item** & **Score** & **Pearson** \\ \hline
1 & 0.49 & **0.67** & 0.49 & 0.54 & **0.71** & 0.41 & 0.30 & 0.66 & 0.63 & 0.57 & **0.79** \\
2 & 0.47 & **0.66** & 0.40 & 0.48 & **0.73** & 0.38 & 0.24 & 0.71 & **0.71** & 0.59 & **0.71** \\
3 & 0.42 & **0.62** & 0.37 & 0.44 & **0.68** & 0.39 & 0.27 & **0.66** & 0.65 & 0.56 & 0.65 \\
4 & 0.43 & **0.56** & 0.38 & 0.45 & **0.63** & 0.38 & 0.26 & 0.61 & 0.61 & 0.53 & **0.62** \\
5 & 0.42 & **0.55** & 0.36 & 0.42 & **0.60** & 0.37 & 0.24 & 0.58 & 0.58 & 0.53 & **0.60** \\
6 & 0.42 & **0.53** & 0.35 & 0.42 & **0.56** & 0.36 & 0.23 & 0.57 & 0.56 & 0.53 & **0.57** \\
7 & 0.44 & **0.52** & 0.36 & 0.44 & **0.54** & 0.35 & 0.25 & 0.54 & 0.54 & 0.50 & **0.54** \\
8 & 0.43 & **0.50** & 0.35 & 0.43 & **0.51** & 0.34 & 0.23 & 0.52 & 0.52 & 0.49 & **0.53** \\
9 & 0.42 & **0.49** & 0.34 & 0.42 & **0.50** & 0.34 & 0.23 & 0.49 & 0.50 & 0.48 & **0.52** \\
10 & 0.41 & **0.47** & 0.34 & 0.41 & **0.49** & 0.33 & 0.23 & 0.48 & 0.47 & 0.47 & **0.50** \\ \hline Avg. & 0.44 & **0.56** & 0.37 & 0.45 & **0.60** & 0.36 & 0.25 & 0.58 & 0.58 & 0.53 & **0.60** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Top-_N_ accuracy for case 3. For further analysis, we randomly select 10 test data and respectively calculate predicted values for the RF user modeling, the RF item modeling, and the RF R-square-based score, as shown in Figure 3, where 1 denotes a purchased item and \(-1\) denotes a non-purchased item.