Despite the complexity of individual behaviors and the absence of an active governor, many social-like systems autonomously exhibit large-scale collective behaviors. Consider human social groups, political bodies, or migrating animals; all of these systems are composed of diverse individual behaviors which are challenging to accurately model en masse. How these systems organize themselves and form collectives is an important topic of current research across many fields.
To begin analyzing a complex system, we seek to define the large-scale variables describing the emergent behavior of the system. In this talk we will discuss the application of diffusion maps to high-dimensional, noisy data, in order to reduce dimensions and formulate macroscopic variables for a system of interacting agents. Using this method we formulate a statistical test for detecting emergent macro-scale relationships between variables, allowing us to both detect system-wide organization among variables measured at the micro-scale, as well as discern between different modes of organization.
As an example application we study the schooling behavior of 300 fish, recorded in a lab setting. We are able to discern between the three main modes of group (dis)organization without defining any macroscale variables, as well as create a risk measure to detect the individuals most likely to drive a regime shift of the system as a whole.