Analyzing collective motion with machine learning and topology

Bhaskar, Dhananjay; Manhart, Angelika; Milzman, Jesse; Nardini, John T.; Storey, Kathleen M.; Topaz, Chad M.; Ziegelmeier, Lori

doi:10.1063/1.5125493

Cited by 40 publications

(32 citation statements)

References 41 publications

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“…As was the case with the zonal model, all simulations were performed over an unbounded domain. Previous work with the ODE model suggests that emergent behaviour stabilises by around 2000 simulation time steps, [ 45 ], albeit for larger groups with N = 200, and for calculations run with time steps of 0.05 units. The same study also notes that the model of [ 22 ] typically behaves independent of initial conditions, [ 45 ], but for our work we found multiple group-level patterns of movement emerging for the same set of model parameters (as noted in Table 3 ).…”

Section: Numerical Investigationmentioning

confidence: 99%

“…Previous work with the ODE model suggests that emergent behaviour stabilises by around 2000 simulation time steps, [ 45 ], albeit for larger groups with N = 200, and for calculations run with time steps of 0.05 units. The same study also notes that the model of [ 22 ] typically behaves independent of initial conditions, [ 45 ], but for our work we found multiple group-level patterns of movement emerging for the same set of model parameters (as noted in Table 3 ). Where possible we sought to generate data from at least 10 realisations (and up to 80) representative of a particular emergent state for given parameter values ( Table 3 ).…”

Section: Numerical Investigationmentioning

confidence: 99%

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Examination of an averaging method for estimating repulsion and attraction interactions in moving groups

Mudaliar

Schaerf

2020

PLoS ONE

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Groups of animals coordinate remarkable, coherent, movement patterns during periods of collective motion. Such movement patterns include the toroidal mills seen in fish shoals, highly aligned parallel motion like that of flocks of migrating birds, and the swarming of insects. Since the 1970’s a wide range of collective motion models have been studied that prescribe rules of interaction between individuals, and that are capable of generating emergent patterns that are visually similar to those seen in real animal group. This does not necessarily mean that real animals apply exactly the same interactions as those prescribed in models. In more recent work, researchers have sought to infer the rules of interaction of real animals directly from tracking data, by using a number of techniques, including averaging methods. In one of the simplest formulations, the averaging methods determine the mean changes in the components of the velocity of an individual over time as a function of the relative coordinates of group mates. The averaging methods can also be used to estimate other closely related quantities including the mean relative direction of motion of group mates as a function of their relative coordinates. Since these methods for extracting interaction rules and related quantities from trajectory data are relatively new, the accuracy of these methods has had limited inspection. In this paper, we examine the ability of an averaging method to reveal prescribed rules of interaction from data generated by two individual based models for collective motion. Our work suggests that an averaging method can capture the qualitative features of underlying interactions from trajectory data alone, including repulsion and attraction effects evident in changes in speed and direction of motion, and the presence of a blind zone. However, our work also illustrates that the output from a simple averaging method can be affected by emergent group level patterns of movement, and the sizes of the regions over which repulsion and attraction effects are apparent can be distorted depending on how individuals combine interactions with multiple group mates.

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Section: Numerical Investigationmentioning

confidence: 99%

Section: Numerical Investigationmentioning

confidence: 99%

Examination of an averaging method for estimating repulsion and attraction interactions in moving groups

Mudaliar

Schaerf

2020

PLoS ONE

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“…How can one summarize this much geometric content for use in machine learning tasks, say to predict how the motion of the flock will vary next, or to predict some of the parameters in a mathematical model approximately governing the motion of the birds? Persistent homology has been used in Topaz et al (2015), Ulmer et al (2019), Bhaskar et al (2019), Adams et al (2020b), and Xian et al (2020) to reduce a large collection of geometric content down to a concise summary. These datasets of animal swarms do not lie along beautiful manifolds (global shapes), but nevertheless there is a wealth of information in the local geometry as measured by the short persistent homology bars.…”

Section: Examples Measuring Local Geometrymentioning

confidence: 99%

Topology Applied to Machine Learning: From Global to Local

Adams

Moy

2021

Front. Artif. Intell.

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Through the use of examples, we explain one way in which applied topology has evolved since the birth of persistent homology in the early 2000s. The first applications of topology to data emphasized the global shape of a dataset, such as the three-circle model for 3 × 3 pixel patches from natural images, or the configuration space of the cyclo-octane molecule, which is a sphere with a Klein bottle attached via two circles of singularity. In these studies of global shape, short persistent homology bars are disregarded as sampling noise. More recently, however, persistent homology has been used to address questions about the local geometry of data. For instance, how can local geometry be vectorized for use in machine learning problems? Persistent homology and its vectorization methods, including persistence landscapes and persistence images, provide popular techniques for incorporating both local geometry and global topology into machine learning. Our meta-hypothesis is that the short bars are as important as the long bars for many machine learning tasks. In defense of this claim, we survey applications of persistent homology to shape recognition, agent-based modeling, materials science, archaeology, and biology. Additionally, we survey work connecting persistent homology to geometric features of spaces, including curvature and fractal dimension, and various methods that have been used to incorporate persistent homology into machine learning.

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“…More recently, the use of topological data analysis (TDA) has also entered the mix, to help address some of these questions. The examples provided by [82][83][84][85] show how TDA can be applied even more effectively than the traditional physicsbased order parameters to compare data and model output. Such novel methods could help to begin addressing questions where model hypotheses are to be compared with observed behavior.…”

Section: From Single To Collective Cell Behaviormentioning

confidence: 99%

Bridging from single to collective cell migration: A review of models and links to experiments

Buttenschön

Edelstein‐Keshet

2020

PLoS Comput Biol

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Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular signaling that regulates cell shape and movement, single cell motility, and collective cell behavior from a few cells to tissues. We survey recent literature to summarize distinct computational methods (phase-field, polygonal, Cellular Potts, and spherical cells). We discuss models that bridge between levels of organization, and describe levels of detail, both biochemical and geometric, included in the models. We also highlight links between models and experiments. We find that models that span the 3 levels are still in the minority.

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Analyzing collective motion with machine learning and topology

Cited by 40 publications

References 41 publications

Examination of an averaging method for estimating repulsion and attraction interactions in moving groups

Examination of an averaging method for estimating repulsion and attraction interactions in moving groups

Topology Applied to Machine Learning: From Global to Local

Bridging from single to collective cell migration: A review of models and links to experiments

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