Estimating The Optimal Cluster Number For Vehicular Network Using Scott's Formula

Selecting the correct cluster number for K-Clustering algorithms such as K-Medoids is essential for optimal output. The Elbow and Silhouette methods are usually used to select the optimal K number for clustering. However, the high computational complexity makes these methods inefficient in Vehicular Network (VN) environment. Therefore, an efficient K estimating technique is essential for an effective VN clustering scheme. K-medoids algorithm is a Machine Learning clustering algorithm usually implemented by the road infrastructure in the VN. The algorithm selects cluster medoids that minimize the sum of dissimilarities between cluster members and their respective medoids. This paper proposes using Scott's histogram formula for bin numbers to calculate the optimal K number. Estimating the underlying probability density function of the data can give a good approximation of the K number for the K-Medoids algorithm. The clustering algorithm is simulated using OMNET++ and Veins simulators in a VN environment. Using Scott's formula, picking the optimal K number is evaluated against the Elbow method in different traffic density and vehicular speed scenarios. Scott's formula gave a close estimate of the K number when implemented using vehicle coordinates.