# New RFI Model for Behavioral Audience Segmentation in Wi-Fi Advertising System
## 2 Related Works
### Performance Evaluation Metrics  
As clustering is an unsupervised machine learning algorithm, the assessment of similarity or dissimilarity is used to evaluate the performance of clustering [32]. By locating disparate data points and combining related data points, the clustering algorithms can perform well. The elbow method, silhouette score, Calinski-Harabasz Index, as well as the Dunn Index are four widely used evaluation metrics for assessing the quality of clusters. The elbow method's underlying theory says that the mean of the entire within-cluster sum of square error (SSE) should be as small as possible. The distortion score, which is an average of SSE, is calculated as the sum of the squared distances between each data point and the cluster centroid. Each cluster's compactness serves as a gauge for the SSE [33]. The cluster is more compact and has less fluctuation when the SSE value is lower. The elbow point, as seen in the graph below, serves as the graph's pivot point and is the definition of this method's arm structure. The elbow point that was discovered shows the correct number of clusters (k). According to [34], the silhouette score determines the consistency within the data clusters. The silhouette score is employed to quantify the separation of clusters in terms of their spatial separation. It shows how closely connected each data point in a cluster is to those in the nearby clusters. The value range for evaluating the performance of the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Categories** & **Algorithm** & **Key Characteristic** \\ \hline \multirow{2}{*}{Centroid based} & \multirow{2}{*}{K-means [29]} & Partitioning the data into k clusters \\  & & based on the centroid of cluster \\ \hline \multirow{2}{*}{Hierarchical based} & \multirow{2}{*}{Agglomerative Hierarchical Clustering [30]} & Recursively merging the nearest pair of \\  & & data or clusters to generate a hierarchy \\ \hline \multirow{2}{*}{Model based} & Gaussian Mixture Model (GMM) [31] & Estimating the probabilities of each \\  & (GMM) [31] & data belonging to each cluster \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Clustering algorithms in different categories. silhouette score is from \(-1\) to \(1\). Incorrect cluster assignment is denoted by \(-1\), whereas \(0\) denotes no discernible distance between clusters, making it difficult to distinguish between them. A large distance between clusters is denoted by \(1\), indicating well-defined clusters. As a result, one of the iterations of the silhouette coefficient closest to \(1\) will be used to determine how many clusters, which is the _optimal cluster_ (k) to be used. The Calinski-Harabasz Index (CH Index) is a metric that is utilized to measure the similarity of cohesion compared to separation [35]. Cohesion refers to the distance of a data point to its own cluster. The cohesion is measured by summing the distances between each data point of the cluster and its own centroid. The separation is the measure of how far the cluster centroids are from the global centroid and is measured by summing up the distances from each centroid of clusters to the global centroid of the dataset. The CH Index is measured by the separation divided by cohesion. The higher the score of the CH Index, the stronger the cohesiveness of the cluster. Another measurement for assessing the robustness of the clustering performance is the Dunn Index. The Dunn Index is evaluated using an internal evaluation schema, and the clustered data are used to obtain the final result [36]. The purpose of the Dunn Index is to determine the compaction and variation in the clusters, similar to the other evaluation metrics. It will be able to distinguish between clusters with a high inter-cluster distance from those with a low intra-cluster distance. The value of the smallest intra-cluster distance divided by the largest inter-cluster distance produces the Dunn Index.