## 4 Experiments
### Evaluation Results
This has shown that user-based collaborative filtering that uses two groups of users' ratings (friends and natives) to generate recommendations can achieve a lower error rate(i.e., higher accuracy) than IBCF, UBCF, and PersMean approaches. For further analysis of the results, we show a box and whisker plot in Figure 5 with Friedman test results. Note that a \(p\) value <0.05 means the experimental result in Table 5 is statistically significant. Again, we applied pairwise Wilcoxon signed-rank tests to identify which pairs were significant. Table 6 shows the pairwise Wilcoxon signed-rank test of RMSE. It can be seen that FANA-IBCF significantly outperformed all other algorithms. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **UBCF** & **PersMean** & **FANA-IBCF** & **FANA-UBCF** \\ \hline IBCF & **0.062** & **0.062** & 0.125 & **0.062** \\ UBCF & - & **0.062** & **0.062** & 0.181 \\ PersMean & - & - & **0.062** & **0.062** \\ FANA-IBCF & - & - & - & **0.062** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Pairwise Wilcoxon signed-rank test of MAE performance among IBCF, UBCF, PersMean, and our proposed approach, FANA-CF. The results in bold are statistically significant with a 90% confidence level. Figure 4: Box and whisker plot of MAE with Friedman test results. Note that a \(p\) value < 0.05 means the experimental result is statistically significant. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **UBCF** & **PersMean** & **FANA-IBCF** & **FANA-UBCF** \\ \hline IBCF & **0.062** & **0.062** & **0.062** & **0.062** \\ UBCF & - & **0.062** & **0.062** & 0.181 \\ PersMean & - & - & **0.062** & **0.062** \\ FANA-IBCF & - & - & - & **0.062** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Pairwise Wilcoxon signed-rank test of RMSE performance among IBCF, UBCF, PersMean, and our proposed approach, FANA-CF. The results in bold are statistically significant with a 90% confidence level. Figure 5: Box and whisker plot of RMSE with Friedman test results. Note that a \(p\) value < 0.05 means the experimental result is statistically significant. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Experiment \#** & **IBCF** & **UBCF** & **PersMean** & **FANA-IBCF** & **FANA-UBCF** \\ \hline
1 & 19.119 & 17.200 & 22.692 & 18.927 & 17.199 \\
2 & 17.773 & 16.389 & 23.267 & 17.695 & 16.381 \\
3 & 19.780 & 17.715 & 24.193 & 18.776 & 17.715 \\
4 & 16.841 & 16.367 & 23.162 & 16.824 & 16.367 \\
5 & 18.782 & 16.820 & 23.210 & 18.779 & 16.796 \\ Average & 18.459 \(\pm\) 1.037 & 16.898 \(\pm\) 0.511 & 23.3045 \(\pm\) 0.489 & 18.200 \(\pm\) 0.818 & **16.892 \(\pm\) 0.513** \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of root mean squared error (RMSE) performance among IBCF, UBCF, PersMean, and our proposed approach, FANA-CF, using 5-fold cross validation. We have calculated the average RMSE and the standard deviation for each approach. Friedman test results. Note that a \(p\) value \(<\) 0.05 means the experimental result in Table 7 is statistically significant. Table 8 shows the pairwise Wilcoxon signed-rank test of nDCG. We can see that our algorithms (FANA-IBCF and FANA-UBCF) are still comparable to other algorithms.