A Computational Topology-based Spatiotemporal Analysis Technique for Honeybee Aggregation

TL;DR

This paper introduces a topological data analysis method using CROCKER matrices to analyze honeybee group behavior, successfully identifying phases of aggregation and dispersion in both synthetic and real data.

Contribution

The paper presents a novel application of topological summaries and change-point detection to characterize honeybee collective behavior over time.

Findings

Identified distinct phases of honeybee aggregation and dispersion.

Successfully applied the method to both synthetic and laboratory data.

Detected an additional phase change indicating complex group dynamics.

Abstract

A primary challenge in understanding collective behavior is characterizing the spatiotemporal dynamics of the group. We employ topological data analysis to explore the structure of honeybee aggregations that form during trophallaxis, which is the direct exchange of food among nestmates. From the positions of individual bees, we build topological summaries called CROCKER matrices to track the morphology of the group as a function of scale and time. Each column of a CROCKER matrix records the number of topological features, such as the number of components or holes, that exist in the data for a range of analysis scales at a given point in time. To detect important changes in the morphology of the group from this information, we first apply dimensionality reduction techniques to these matrices and then use classic clustering and change-point detection algorithms on the resulting scalar data. A test of this methodology on synthetic data from an agent-based model of honeybees and their trophallaxis behavior shows two distinct phases: a dispersed phase that occurs before food is introduced, followed by a food-exchange phase during which aggregations form. We then move to laboratory data, successfully detecting the same two phases across multiple experiments. Interestingly, our method reveals an additional phase change towards the end of the experiments, suggesting the possibility of another dispersed phase that follows the food-exchange phase.