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Additional support was provided by the National Oceanic and Atmospheric Administration award NOAA-AWD100582 (GH), the Simons Foundation Grant 395890 (GH), and the National Science Foundation Grant OCE-184857 (GH). įunding: This project was funded by the DARPA Young Faculty Award number N6-4038 (MT, GH, JW).
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This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.ĭata Availability: All relevant data is available in a public repository. Received: MaAccepted: NovemPublished: February 12, 2021Ĭopyright: © 2021 Titus et al. PLoS Comput Biol 17(2):Ībdus Salam International Centre for Theoretical Physics, ITALY We show that our state classification subdivides the known behaviors of the school in a meaningful manner, leading to a finer description of the system’s behavior.Ĭitation: Titus M, Hagstrom G, Watson JR (2021) Unsupervised manifold learning of collective behavior. This method is demonstrated on a synthetic flocking model as well as empirical fish schooling data. Using these covariances we discern between different modes of collective behavior in a data-driven, unsupervised manner. Additionally, the form of the macro-scale organization is encoded in the covariances among the two sets of diffusion map components. A large MAS is evidence that the two networks are codetermined in some fashion, indicating an emergent relationship between the metrics d (1) and d (2). Comparing these geometries, we formulate a measure of similarity between two networks, called the map alignment statistic (MAS). We apply the method of diffusion maps to the systems ( X, d ( i)) to recover efficient embeddings of their interaction networks. We require only metrics, d (1), d (2), defined on the set of agents, X, which measure agents’ nearness in variables of interest. Here, we present a new unsupervised method of detecting emergent behavior in complex systems, and discerning between distinct collective behaviors. This presents a challenge for studying novel systems where there may be little prior knowledge. Each of these cases requires knowledge of and a method for characterizing the macro-state(s) of the system. Characterizing modes of collective behavior is often done through human observation, training generative models, or other supervised learning techniques. Collective behavior is an emergent property of numerous complex systems, from financial markets to cancer cells to predator-prey ecological systems.