BUNCH: A Hierarchical Filtering Algorithm for Identifying Persistent Entities in Interactive Particle Systems

Detecting trajectories of hierarchical structures in a dynamical system of multiple interacting particles is an open problem that is typically addressed by imposing strong constraints on the structures to be found. Here, we describe BUNCH, a dynamical filtering algorithm that can efficiently and on-the-fly fit dynamical trajectories of multiple particles to a tree structure of Gaussian clusters that can model a wide range of hierarchically arranged structures, while extracting and calculating hierarchical properties such as complexity, lifespan, and other information- and time-based properties of an entity (an object defined by its structure) and of all of its constituting subentities. Unlike other (hierarchical) clustering algorithms, BUNCH emphasizes independence from adjustable parameters and ascribes equal importance to each hierarchy level and its attending attributes, of the tree of clusters that best fits an evolving particle system. We illustrate the performance of BUNCH via an operational definition of “lifeness” of an entity, as the product of its defining information (algorithmic complexity) integrated over its lifetime, in units of information × time. Thus we provide a proof of concept that measuring and quantifying level-wise properties of hierarchically modeled systems with BUNCH is feasible for small enough particle systems, thereby enabling the classification of entities and subentities via the measurement of hierarchical properties.