Visualization and Cluster Analysis of Dynamic Reference Graphs

A novel method for cluster analysis is developed. The method finds a dynamic composite “supercluster” for data changing with time. A supercluster consists of two non-overlapping parts: the core and the shell. The core is a set of elements that are connected to each other more than to elements of the shell. We assume that the core of a dynamic supercluster is constant, whereas shells may vary in time. We build an approximation model for the dynamic composite supercluster and derive the optimal values for its parameters. An iterative method is developed for finding such superclusters for temporal proximity matrices. The algorithm applies to the analysis of the dynamic reference graphs. A dynamic reference graph is a graph whose vertices are key-phrases provided for a collection of texts indexed by time. Its directed edges are labeled with weights expressing the degree of association between the key-phrases according to the texts in the collection. Therefore, applying our algorithm we can find a core corresponding to terms that are interconnected through all the time, and shells corresponding to specific time-periods. We provide a tool for visualization of dynamic reference graphs. In the end, two dynamic graphs are analyzed. The first refers to a collection of newspaper articles on issues of economics in Russian (2014-15), and the second is based on the phantasy novel “A song of ice and fire” by G.R.R. Martin.