A Reductionist Approach to Hypothesis-Catching for the Analysis of Self-Organizing Decision-Making Systems

Abstract

A difficulty in analyzing self-organizing decision-making systems is their high dimensionality which needs to be reduced to allow for deep insights. Following the hypothesis that such a dimensionality reduction can only be usefully determined in an act of a low-scale scientific discovery, a recipe for a data-driven, iterative process for determining, testing, and refining hypotheses about how the system operates is presented. This recipe relies on the definition of Markov chains and their analysis based on an urn model. Positive and negative feedback loops operating on global features of the system are detected by this analysis. The workflow of this analysis process is shown in two case studies investigating the BEECLUST algorithm and collective motion in locusts. The reported recipe has the potential to be generally applicable to self-organizing collective systems and is efficient due to an incremental approach.

Swarm in a Fly Bottle: Feedback-Based Analysis of Self-organizing Temporary Lock-ins

“…In experiments, the complexity of the collective motion is reduced to a pseudo-1-d setting by using a ring-shaped arena. Microscopic [Czirók et al, 1999] and macroscopic models [Yates et al, 2009, Hamann, 2012, 2013b of this behavior have been reported. Here we use the microscopic model of self-propelled particles by Czirók et al [1999] as our reference model (henceforth 'Czirók model').…”

“…In the locust scenario, the first priority for the swarm is to achieve alignment which is generally independent of agents' positions. However, locusts seem to depend heavily on spatial features such as the number of neighbors [Hamann, 2013b]. In the following, we briefly investigate the difference between well-mixed systems and systems whose agents' spatial distributions are biased by agents' headings.…”

“…A swarm is a distributed agent system where each agent autonomously decides on its actions. With the global knowledge of an external observer, we can classify at least a subset of these actions as positive or negative feedback events that drive the system, respectively, towards or away from a too ordered state [Hamann, 2012[Hamann, , 2013b. By counting these events we are able to calculate the ratio of positive feedback events f + = F + F + +F − , for the number of positive feedback events 0 ≤ F + ≤ N for swarm size N (F − accordingly).…”

“…If f + > 0.5 we say positive feedback is predominant. For several swarm systems, such as density classification, aggregation controlled by BEECLUST, and alignment in locust swarms, negative feedback is initially predominant while positive feedback builds up only over time and independently of the order of the current system state [Hamann, 2012[Hamann, , 2013b. Consequently, there exists a second feature and/or a mechanism besides the order of the system that controls the increase of positive feedback intensity.…”