## 4 Performance Evaluation Results and Discussion
### Considering Normalization of Components in User Influence, User Activity  
Each of the different components of the user influence and user activity are dependent upon the social network data characteristics and could have a significantly different range of values. For instance, some components may be in the range of 0 to 1 while others may be in the range of 1000 to 3000. This significant difference in the range of values for the components could impact the calculation results of the user influence and user activity. To provide a way to adjust the range of values for the components, a configurable parameter \(\beta\) that normalizes the component value is provided. Additional experiments have been carried out to analyze the effect of normalizing the components of the user influence and user activity. The configurable parameter \(\beta\) is set to the inverse of the maximum value of each component, respectively. This will allow the component value to be scaled to a value \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Concept** & **Influence** & **Activity** & \begin{tabular}{c} **Num** \\ **Elite** \\ \end{tabular} & \begin{tabular}{c} **Num** \\ **Fans** \\ \end{tabular} & \
\begin{tabular}{c} **Num** \\ **Friends** \\ \end{tabular} &
\begin{tabular}{c} **Num** \\ **Reviews** \\ \end{tabular} & **Recent Date** \\ \hline Influence & 1 & 0.141479 & 0.485973 & 0.993308 & 0.4809687 & 0.14866026 & \(-\)0.09194966 \\ Activity & 0.141479 & 1 & 0.24435 & 0.119344 & 0.35697629 & 0.70084475 & 0.14612793 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Correlations between user influence, user activity, and the Yelp variables. Figure 8: Evaluation difference between the top 10 users with a large number of friends and the average of all users: (**a**) the difference is shown for each restaurant; (**b**) the average evaluation difference is shown for each top 10 users with a large number of friends. that is within the range of 0 to 1. For the user influence, the parameter values were set as \(\beta_{1}\) = 1.0, \(\beta_{2}\) = 0.1, \(\beta_{3}\) = 1.0, and \(\beta_{4}\) = 1.125. For the user activity, the parameter values were set as \(\beta_{1}\) = 1.125, \(\beta_{2}\) = 0.0001, and \(\beta_{3}\) = 1.1618. The configurable parameters \(\alpha\) that were used to assign weights were all set to 1. The user influence and user activity for all the 55,452 users were calculated and the top 10 influential users and top 10 active users were selected. Figure 9 shows each of the top 10 influential user evaluations compared against the average evaluation of all users for each of the 10 or less restaurants most recently reviewed by the top 10 influential users. Figure 9: Comparison of the evaluations by the top 10 influential users with the average evaluations by all users. The results show that the top 10 influential users make evaluations quite close to the average of all the users' evaluations, within a difference of \(-1\) to +1. However, the selected users show some limitations, such as the number of reviews written by the users being very small, so in many cases only one restaurant could be included in the comparison. This makes it very hard to decisively conclude that these top 10 influential users' evaluations are credible. Figure 10 shows a comparison graph for each of the top 10 active users. Each of the evaluations of the top 10 active users are compared against the average evaluation of all users for each of the 10 or less restaurants most recently reviewed by each of the top 10 active users. The results show that the evaluations by the top 10 active users are significantly different from the average evaluations by all users. The results verify that the pure normalization may not be sufficient for the selection of credible active users. Figure 10: Comparison of the evaluations by the top 10 active users with the average evaluations by all users.