Determination of the optimal number of clusters using a spectral clustering optimization

In this paper, we present a new method, called Spectral Global Silhouette method (GS), to calculate the optimal number of clusters in a dataset using a Spectral Clustering algorithm. It combines both a Silhouette Validity Index and the concept of Local Scaling. First, the GS algorithm has first been tested using synthetic data. Then, it is applied on real data for image segmentation task. In addition, three new methods for image segmentation and two new ways to calculate the optimal number of groups in an image are proposed. Our experiments have shown a promising performance of the proposed algorithms.