Unsupervised manifold learning of collective behavior.

Area of Science:

• Complex Systems Science
• Network Science
• Data Science

Background:

• Collective behavior is an emergent property in various systems, often studied using supervised methods requiring prior knowledge of system macro-states.
• Characterizing novel systems with limited prior information presents a significant challenge in understanding collective dynamics.

Purpose of the Study:

• To develop a novel unsupervised method for detecting emergent behavior and discerning distinct collective behaviors in complex systems.
• To enable the study of systems where prior knowledge of macro-states is limited.

Main Methods:

• Utilized diffusion maps on agent interaction networks defined by nearness metrics (d(1), d(2)).
• Introduced the map alignment statistic (MAS) to measure network similarity and infer emergent relationships between metrics.
• Analyzed covariances of diffusion map components to discern macro-scale organization and classify collective behaviors.

Main Results:

• Demonstrated the method's effectiveness on synthetic flocking models and empirical fish schooling data.
• Showcased the ability to identify emergent relationships between different agent interaction metrics.
• Successfully classified distinct modes of collective behavior in fish schooling, providing a finer description of system dynamics.

Conclusions:

• The proposed unsupervised method effectively detects and classifies emergent collective behaviors in complex systems.
• This approach offers a data-driven alternative to supervised methods, particularly valuable for novel or poorly understood systems.
• The technique provides a more granular understanding of system dynamics by subdividing known behaviors into meaningful states.