This algorithm makes use of the same evaluation function that is used by a hierarchical algorithm during clustering to construct an evaluation graph where the x-axis is the number of clusters, and the y-axis is the value of the evaluation function at x clusters. The point of the maximum curvature of this graph is used as the number of clusters to return. This point is determined by finding the area between the two lines that most closely fit the curve [23]. However, this method works poorly with mixed data types, and it does not work well on very large data sets. In this paper, we introduce the density peaks algorithm, which has the ability to recognize clusters regardless of their shape. The clustering is performed using the efficient evolutionary spectral clustering algorithm, and we adapted the density peaks clustering algorithm to automatically find the number of clusters, which dynamically changes over time. This algorithm is based on the assumptions that the cluster centers are surrounded by neighbors with a lower local density and that they also have relatively large distances from other data points with a higher local density. It also has the advantage of visualizing the structure of the data in the decision graph. The proposed algorithm is compared with the modularity and the eigengap methods to show its effectiveness. The new contributions of this paper are summarized as follows:  
* We optimize the efficient evolutionary spectral clustering algorithm in order to cluster real world traffic data sets collected from the transportation network of Amsterdam city [17]. This algorithm was built in order to handle traffic evolving over time. * We extend this algorithm for the preserving cluster membership framework by computing a new sparse similarity matrix that considers traffic at previous times. We show that this algorithm minimizes time and space complexities. We prove that the proposed efficient evolutionary spectral clustering algorithm provides more robustness and effectiveness compared with other static clustering methods in the case of a transportation network. * We compute the number of clusters for each time period using the density peak algorithm. We modify this algorithm in order to compute the distance between snakes based on the sparse snake similarity matrix. This algorithm is proven to be more effective than the modularity and the eigengap methods in the case of efficient evolutionary spectral clustering. * We convert the transportation network into different graph models in order to find directional congestion. We study the evolution of the graph over different time periods of the day. We prove which clustering method is the most efficient for clustering all time-dependent road speed observations into 3D speed maps, and we study the computational times to partition the road network. The paper is structured as follows: in Section 2, we present the graph models and how to compute the similarity matrix. We also introduce the spectral clustering algorithm ans the evolutionary spectral clustering algorithm, and we propose an efficient evolutionary spectral clustering algorithm for the partitioning of a transportation network. In Section 3, we explain how to automatically find the number of clusters using the density peak algorithm. Section 4 shows the experimental results, and finally the paper is summarized with our conclusions in Section 5.