# New RFI Model for Behavioral Audience Segmentation in Wi-Fi Advertising System
## 5 Discussion  
The RFI model was used to understand the behavior of the audience towards the effect of advertising. Table 5 shows the average values of recency, frequency, and interest level in each cluster of the two most active campaigns for the normal case, whereas Table 6 illustrates the special case. To provide a more comprehensive representation of the audience behavioral patterns, a dynamic characteristics range is created in Table 7, elaborating on the behavior of the audience groups mentioned in Tables 5 and 6. The dynamic characteristics range table is established based on similar practices from [38; 39], by dividing all the RFI values for a campaign into four quartiles. In Table 7, five characteristics are defined based on the non-negative RFI values, ranging from zero to positive infinity, with the initial characteristics for each metric set to zero. The subsequent characteristics of each metric are defined according to different quartiles, where the upper limit of each quartile is determined by 25%, 50%, and 75%. As the characteristic range table is generated dynamically from \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case** & **Campaign** & **Clustering Algorithm** & **Elbow Method** & **Silhouette Score** & **CH Index** & **Dunn Index** \\  & & & \(\downarrow\) & \(\uparrow\) & \(\uparrow\) & \(\uparrow\) \\ \hline \multirow{4}{*}{Normal case} & \multirow{4}{*}{764} & K-means & **17,179.932** & **0.512** & **12,127.681** & 0.337 \\  & & Agglomerative hierarchical & 23,695.748 & 0.459 & 9911.987 & 0.734 \\  & & Gaussian Mixture Model & 34,949.082 & 0.143 & 6897.579 & **0.771** \\ \cline{2-7}  & & \multirow{4}{*}{776} & K-means & **16,297.157** & **0.511** & **12,658.076** & 0.393 \\  & & Agglomerative hierarchical & 17,555.738 & 0.495 & 11,400.780 & 0.375 \\  & & Gaussian Mixture Model & 34,077.653 & 0.419 & 7015.656 & **0.785** \\ \hline \multirow{4}{*}{Special case} & \multirow{4}{*}{764} & K-means & **17,737.915** & **0.501** & **11,590.687** & 0.320 \\  & & Agglomerative hierarchical & 19,004.798 & 0.490 & 10,488.531 & 0.399 \\ \cline{1-1}  & & Gaussian Mixture Model & 38,536.754 & 0.367 & 5750.592 & **0.472** \\ \cline{1-1} \cline{2-7}  & & \multirow{4}{*}{776} & K-means & **17,198.727** & **0.496** & **11,738.731** & 0.349 \\ \cline{1-1}  & & Agglomerative hierarchical & 19,000.083 & 0.480 & 10,163.169 & 0.400 \\ \cline{1-1}  & & Gaussian Mixture Model & 37,381.868 & 0.379 & 5901.983 & **0.499** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance comparison of the clustering algorithms for Campaign 764 and 776. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case** & **Campaign** & **Algorithm** & **Elbow Method** & **Silhouette Score** & **CH Index** & **Dunn Index** \\ \hline \multirow{4}{*}{Normal case} & \multirow{4}{*}{764} & K-means & 5 & 5 & 5 & 3 \\  & & & Agglomerative hierarchical & 5 & 5 & 5 & 4 \\  & & Gaussian Mixture Model & 3 & 5 & 3 & 3 \\ \cline{2-6}  & & \multirow{4}{*}{776} & K-means & 5 & 5 & 5 & 3 \\  & & & Agglomerative hierarchical & 5 & 4 & 5 & 3 \\  & & Gaussian Mixture Model & 3 & 4 & 3 & 3 \\ \hline \multirow{4}{*}{Special case} & \multirow{4}{*}{764} & K-means & 5 & 5 & 5 & 3 \\  & & Agglomerative hierarchical & 4 & 4 & 4 & 4 \\  & & Gaussian Mixture Model & 3 & 5 & 3 & 3 \\ \cline{1-1} \cline{2-6}  & & \multirow{4}{*}{776} & K-means & 5 & 5 & 5 & 3 \\  & & Agglomerative hierarchical & 5 & 5 & 5 & 3 \\  & & Gaussian Mixture Model & 3 & 3 & 3 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Result of optimal cluster evaluation for Campaign 764 and 776.  
the RFI values of each campaign, the actual range will vary depending on the RFI values associated with different campaigns.