Spatial and temporal clustering based on the echelon scan technique and software analysis

In this paper, we propose the details of algorithms for the echelon and the echelon scan techniques for the first time though we have already proposed these techniques through specific numerical examples in previous papers. We also release EcheScan software developed in R and Shiny-server based on this algorithm. Through an internet browser, researchers can access the technologies in web applications. We discuss the clustering and hotspot detection for spatial and temporal lattice data. Our approach is based on the idea of echelon techniques. The echelon dendrogram is a powerful tool to handle any types of lattice data with visualization. Regional features such as hotspots and trends are shown in an echelon dendrogram. The echelon scan technique searches for a hotspot by moving the scanning window in a particular manner. The echelon scan technique is easy to interpret based on regional hierarchical structure of interested values according to visual order. We propose the algorithms to obtain the elements for echelon and the maximum likelihood ratio based on echelon scan given the values of lattice and its neighbors. We also explain the usages of EcheScan software for echelon and echelon scanning. In addition, the echelon technique for two types of lattice data and spatio-temporal epidemiological lung cancer data in New Mexico are illustrated using EcheScan software.