# New RFI Model for Behavioral Audience Segmentation in Wi-Fi Advertising System
## 4 Experiments and Results  
To investigate the audience behavioral patterns towards a single campaign rather than all campaigns collectively, clustering algorithms were applied to analyze audience behavioral patterns within a specific campaign. In this section, both the normal case and the special case of the formulated RFI model are being tested to prove the new RFI model is generally applicable to different advertising attributes. In normal case, the interest metric (I) relies solely on the number of click actions, as suggested in existing research [37]. In contrast, the formulated relationship of total view duration and overall number of clicks received in Equation (4) are utilized in the special case. The recency (R) and frequency (F) metrics remained the same in both cases.  
Both cases are applied to the same dataset and same campaign for performance comparison. The two most active campaigns of the dataset, which is Campaign 764 and Campaign 776, are selected to demonstrate audience segmentation with three clustering algorithms. The three clustering algorithms are k-means clustering, agglomerative hierarchical clustering as well as Gaussian Mixture Model. The characteristics of each cluster and the performance evaluation of each algorithm are elaborated in this section. To perform clustering, identifying the optimal number of clusters is necessary. Four performance evaluation metrics, which are the elbow method, silhouette score, CH Index and Dunn Index are used to determine the optimal number of clusters. Table 3 highlighted the optimal number of clusters for each algorithm in both cases.  
It is not surprising that those clustering algorithms produced different cluster assignments for the same dataset. This could be explained based on the nature of the methodology of clustering algorithms. K-means minimizes the sum of squared distances between the data points and their assigned cluster centroids. Agglomerative hierarchical clustering is a bottom-up approach that starts with each data point as a separate cluster and iteratively merges the closest pairs of clusters until a single cluster containing all data points is obtained. Gaussian Mixture Model is a type of probabilistic model that characterizes data as a combination of multiple Gaussian distributions, where each Gaussian value represents a specific cluster within the data.  
To identify the best-performing clustering algorithm, performance evaluation metrics, which included the silhouette score, CH Index, and Dunn index, were used for comparison, as listed in Table 4. In both cases, k-means outperformed the other two metrics by achieving the lowest score in the elbow method and the highest scores in both silhouette score and CH Index. It was followed by the agglomerative hierarchical and Gaussian Mixture models. For the Dunn Index, the Gaussian Mixture Model obtained the highest score, followed by the agglomerative hierarchical and k-means models. This was because the Gaussian Mixture Model tended to produce more compact and less-separated clusters. It is worth noting that the performance of k-means in the special case was slightly lower than the Gaussian Mixture Model, with a difference of 0.152 in Campaign 764 and 0.150 in Campaign 776.  
Figure 4: Relationship between total view duration and overall number of clicks received in (**a**) Campaign 764 and (**b**) Campaign 776.  
Therefore, k-means clustering is the top-performing algorithm in the overall performance, followed by agglomerative hierarchical, whereas the Gaussian Mixture Model showed the least favorable results. Consequently, the groups segmented by k-means clustering were further analyzed to interpret the segmented audience behaviors based on the RFI model.