# Recommendation System for a Delivery Food Application Based on Number of Orders
## 5 Experiments and Results
### Number of Preferred Restaurants According to the Value of Parameter Pmin  
Since our metric for calculating the recommendations' performance removes one of the preferred restaurants for each client, it is important to know the number of preferred restaurants is modified when varying the parameter of _pmin_ (see Figure 6 and Table 3). It can be observed that by using 5% as the minimum percentage for considering a restaurant as one of the favorites, we have around five restaurants among the client's preferences. As expected, if the value of _pmin_ increases, the number of preferred restaurants decreases. If we consider a minimum percentage of 10% (as recommended), we have around 2.6 preferred restaurants. Based on the dataset used for this research, we do not recommend a value of _pmin_ greater than 0.1 because the number of preferred restaurants is very small (\(\leq\)2). In addition, values smaller than 0.1 indicate that we need less than 10% of our orders to consider a restaurant to be one of our favorites. Figure 6: The average number of preferred restaurants (_y_-axis) according to the value of the parameter _pmin_ (_x_-axis). Vertical lines represent the standard deviation. Figure 7 and Table 4 show that when the value of \(pmin\) increases, the performance of the recommendation system decreases. Moreover, Figure 8 shows that when the value of \(pmin\) increases, the number of recommended restaurants decreases. Those patterns were expected since the bigger the value of \(pmin\), the greater the percentage of orders needed to consider a restaurant a preferred one. An opposite behavior can be observed in the \(k\) parameter (see Figures 7 and 8 and Table 5). In this case, the bigger the value of \(k\), the greater the number of recommendations. In consequence, the better the recommendation system's performance. This is logical because the more clients are considered neighbors, the more chances to obtain restaurants with values bigger than \(pmin\) for recommendations. We need to find a balance of \(k\) because, if we consider a big value, the number of recommended restaurants increases. In a recommendation system, the main idea is to obtain only a few recommendations from a wide range of options. In this case, we set \(k=5\) and \(pmin=0.1\), with an average of 7.7 recommended restaurants and a percentage of correct recommendations of around 0.24. The performance analysis of our recommendation system with the recommended values of parameters (\(pmin\) = 0.1 and \(k=5\)) is presented as follows. The percentage of correct predictions is around 24%. This number may seem small, and the performance of our recommendation system may seem poor. However, Figure 8 and Table 4 show that the average of recommended restaurants is around 7.7, which means that our recommendation system gives the client an average of 7.7 options from 187 available. Moreover, based on our methodology for validation, users have 2.6 preferred restaurants on average. We removed one of them, and 24% of the time our recommendation system can recover it from  
Figure 8: The average number of recommended restaurants (\(y\)-axis) according to the values of the parameters (\(x\)-axis). Vertical lines represent the standard deviation. (**a**) Testing different values for \(pmin\), \(k=5\). (**b**) Testing different values for \(k\), \(pmin\) = 0.1. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Year**} & \multicolumn{6}{c}{**K**} \\ \cline{2-7}  & **3** & **4** & **5** & **6** & **7** & **8** \\ \hline \multicolumn{7}{c}{Average of the percentage of correct recommendations} \\ \hline
2019 & 0.16 & 0.20 & 0.26 & 0.30 & 0.33 & 0.36 \\
2020 & 0.19 & 0.22 & 0.25 & 0.28 & 0.29 & 0.32 \\
2021 & 0.14 & 0.16 & 0.21 & 0.24 & 0.29 & 0.30 \\ \hline \multicolumn{7}{c}{Average of the number of recommended restaurants} \\ \hline
2019 & 4.55 & 6.07 & 7.60 & 8.98 & 10.36 & 11.89 \\
2020 & 4.72 & 6.09 & 7.71 & 9.25 & 10.55 & 11.97 \\
2021 & 4.66 & 6.23 & 7.74 & 9.34 & 10.89 & 12.34 \\ \hline \hline \end{tabular}
\end{table}