Prediction and classification in equation-free collective motion dynamics

Fujii, Keisuke; Kawasaki, Takeshi; Inaba, Yuki; Kawahara, Yoshinobu

doi:10.1371/journal.pcbi.1006545

Cited by 25 publications

(29 citation statements)

References 42 publications

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“…DMD, originally proposed in fluid physics [6,7], has recently attracted attention also in other areas of science and engineering, including analysis of power systems [30], epidemiology [31], neuroscience [9], image processing [8,32], controlled systems [33], and human behaviors [34,35,36]. Moreover, there are several algorithmic variants to overcome the problem of the original DMD such as the use of nonlinear basis functions [37], a formulation in a reproducing kernel Hilbert space [10], in a supervised learning framework via multitask learning [38], in a Bayesian framework [11], and using a neural network [39].…”

Section: Dynamic Mode Decompositionmentioning

confidence: 99%

“…Next, we evaluated our method using a example with unknown global dynamics, because in some real-world (especially biological) data, the true global spatiotemporal structure is sometimes unknown [35,53]. For evaluation, here we used well-known collective motion models [54] with simple local rules to generate multiple distinct group behavioral patterns (Figure 3a): swarm, torus, and parallel behavioral shapes.…”

Section: Fish-schooling Modelmentioning

confidence: 99%

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Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables

Fujii

Kawahara

2019

Neural Networks

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Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been attracting attention as a way of obtaining global modal descriptions of NLDSs without requiring explicit prior knowledge. However, since existing DMD algorithms are in principle formulated based on the concatenation of scalar observables, it is not directly applicable to data with dependent structures among observables, which take, for example, the form of a sequence of graphs. In this paper, we formulate Koopman spectral analysis for NLDSs with structures among observables and propose an estimation algorithm for this problem. This method can extract and visualize the underlying low-dimensional global dynamics of NLDSs with structures among observables from data, which can be useful in understanding the underlying dynamics of such NLDSs. To this end, we first formulate the problem of estimating spectra of the Koopman operator defined in vector-valued reproducing kernel Hilbert spaces, and then develop an estimation procedure for this problem by reformulating tensor-based DMD. As a special case of our method, we propose the method named as Graph DMD, which is a numerical algorithm for Koopman spectral analysis of graph dynamical systems, using a sequence of adjacency matrices. We investigate the empirical performance of our method by using synthetic and real-world data.

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Section: Dynamic Mode Decompositionmentioning

confidence: 99%

Section: Fish-schooling Modelmentioning

confidence: 99%

Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables

Fujii

Kawahara

2019

Neural Networks

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“…Previous works [40,38] have predictively classified the time-varying interactions into two group outcomes (i.e. scored or unscored) while reflecting the timevarying interactions among attackers, defenders and the ball.…”

Section: Introductionmentioning

confidence: 99%

Physically-interpretable classification of biological network dynamics for complex collective motions

Fujii

Takeishi

Hojo

et al. 2020

Sci Rep

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Understanding complex network dynamics is a fundamental issue in various scientific and engineering fields. Network theory is capable of revealing the relationship between elements and their propagation; however, for complex collective motions, the network properties often transiently and complexly change.A fundamental question addressed here pertains to the classification of collective motion network based on physically-interpretable dynamical properties. Here we apply a data-driven spectral analysis called graph dynamic mode decomposition, which obtains the dynamical properties for collective motion classification. Using a ballgame as an example, we classified the strategic collective motions in different global behaviours and discovered that, in addition to the physical properties, the contextual node information was critical for classification. Furthermore, we discovered the label-specific stronger spectra in the relationship among the nearest agents, providing physical and semantic interpretations. Our approach contributes to the understanding of complex networks involving collective motions from the perspective of nonlinear dynamical systems.

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“…In team sports sciences, interpersonal coordination in athletes has been intensively investigated in small-sided [17][18][19] and actual games [8,20,21]. However, the quantitative evaluation of such interpersonal coordination during sports activities in patients with mental disorders has been unknown.…”

Section: Introductionmentioning

confidence: 99%

Cognition and interpersonal coordination of patients with schizophrenia who have sports habits

et al. 2020

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Team sports activities are effective for improving the negative symptoms and cognitive functions in patients with schizophrenia. However, the interpersonal coordination during the sports and visual cognition of patients with schizophrenia who have team sports habits are unknown. The main objectives of this study were to test two hypotheses: first, patients with schizophrenia perform the skill requiring ball passing and receiving worse than healthy controls; and second, the patients will be impaired in these functionings in accordance with the previous studies regarding schizophrenia in general. Twelve patients with schizophrenia and 15 healthy controls, who had habits in football, participated in this study. The participants performed three conventional cognitive tests and a 3-vs-1 ball possession task to evaluate their interpersonal coordination. The results showed that in the 3-vs-1 possession task, the displacement in the pass angle for the patients was significantly smaller than that for the control. The recall in the complex figure test, the performance in the trail making test, and that in the five-choice reaction task for the patients were worse than those for the control. Moreover, we found the significant partial correlations in the patients between the extradimensional shift error and the pass angle as well as between the time in the trail making test and the displacement in the pass angle, whereas there was no significant correlation in the control group. This study clarified the impaired interpersonal coordination during team sports and the visual cognition of patients with schizophrenia who have team sports habits.

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Prediction and classification in equation-free collective motion dynamics

Cited by 25 publications

References 42 publications

Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables

Dynamic mode decomposition in vector-valued reproducing kernel Hilbert spaces for extracting dynamical structure among observables

Physically-interpretable classification of biological network dynamics for complex collective motions

Cognition and interpersonal coordination of patients with schizophrenia who have sports habits

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