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Spatio-temporal modeling of the topology of swarm behavior with persistence landscapes

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Christopher B. JonesAuthors Info & Claims

SIGSPACIAL '16: Proceedings of the 24th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems

Article No.: 65, Pages 1 - 4

https://doi.org/10.1145/2996913.2996949

Published: 31 October 2016 Publication History

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Abstract

We propose a method for modeling the topology of swarm behavior in a manner which facilitates the application of machine learning techniques such as clustering. This is achieved by modeling the persistence of topological features, such as connected components and holes, of the swarm with respect to time using zig-zag persistent homology. The output of this model is subsequently transformed into a representation known as a persistence landscape. This representation forms a vector space and therefore facilitates the application of machine learning techniques. The proposed model is validated using a real data set corresponding to a swarm of 300 fish. We demonstrate that it may be used to perform clustering of swarm behavior with respect to topological features.

References

[1]

H. Adams, S. Chepushtanova, T. Emerson, E. Hanson, M. Kirby, F. Motta, R. Neville, C. Peterson, P. Shipman, and L. Ziegelmeier. Persistence images: An alternative persistent homology representation. arXiv preprint arXiv:1507.06217, 2015.

Google Scholar

[2]

P. Bubenik. Statistical topological data analysis using persistence landscapes. The Journal of Machine Learning Research, 16(1):77--102, 2015.

Digital Library

Google Scholar

[3]

G. Carlsson and V. De Silva. Zigzag persistence. Foundations of computational mathematics, 10(4):367--405, 2010.

Digital Library

Google Scholar

[4]

G. Carlsson, V. De Silva, and D. Morozov. Zigzag persistent homology and real-valued functions. In Proceedings of the twenty-fifth annual symposium on Computational geometry, pages 247--256, 2009.

Digital Library

Google Scholar

[5]

H. Edelsbrunner and J. Harer. Computational topology: an introduction. American Mathematical Soc., 2010.

Google Scholar

[6]

M. Berger, L. M. Seversky, and D. S. Brown. Classifying Swarm Behavior via Compressive Subspace Learning. In IEEE International Conference on Robotics and Automation, Stockholm, Sweden, 2016.

Crossref

Google Scholar

[7]

P. Corcoran, P. Mooney, and G. Huang. Unsupervised Trajectory Compression. In IEEE International Conference on Robotics and Automation, Stockholm, Sweden, 2016.

Google Scholar

[8]

C. M. Topaz, L. Ziegelmeier, and T. Halverson. Topological data analysis of biological aggregation models. PloS one, 10(5):e0126383, 2015.

Crossref

Google Scholar

[9]

K. Tunstrøm, Y. Katz, C. C. Ioannou, C. Huepe, M. J. Lutz, and I. D. Couzin. Collective states, multistability and transitional behavior in schooling fish. PLoS Comput Biol, 9(2):e1002915, 2013.

Crossref

Google Scholar

[10]

J. Werfel, K. Petersen, and R. Nagpal. Designing collective behavior in a termite-inspired robot construction team. Science, 343(6172):754--758, 2014.

Crossref

Google Scholar

[11]

M. Worboys and M. Duckham. Monitoring qualitative spatiotemporal change for geosensor networks. International Journal of Geographical Information Science, 20(10):1087--1108, 2006.

Crossref

Google Scholar

Cited By

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Corcoran PJones C(2023)Topological data analysis for geographical information science using persistent homologyInternational Journal of Geographical Information Science10.1080/13658816.2022.215565437:3(712-745)Online publication date: 4-Jan-2023
https://doi.org/10.1080/13658816.2022.2155654
Corcoran PJones C(2021)A persistent homology model of street network connectivityTransactions in GIS10.1111/tgis.1284426:1(155-181)Online publication date: 27-Oct-2021
https://doi.org/10.1111/tgis.12844
Kim WMémoli F(2021)Generalized persistence diagrams for persistence modules over posetsJournal of Applied and Computational Topology10.1007/s41468-021-00075-1Online publication date: 5-Aug-2021
https://doi.org/10.1007/s41468-021-00075-1
Show More Cited By

Index Terms

Spatio-temporal modeling of the topology of swarm behavior with persistence landscapes
1. Information systems
  1. Information systems applications
    1. Spatial-temporal systems
      1. Geographic information systems
2. Mathematics of computing
  1. Continuous mathematics
    1. Topology
      1. Algebraic topology

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Published In

SIGSPACIAL '16: Proceedings of the 24th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems

October 2016

649 pages

ISBN:9781450345897

DOI:10.1145/2996913

General Chairs:
Mohamed Ali
University of Washington, Tacoma
,
Shawn Newsam
University of California, Merced
,
Program Chairs:
Matthias Renz
George Mason University, USA
,
Goce Trajcevski
Northwestern University, USA
,
Siva Ravada
Oracle Corporation, USA

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 31 October 2016

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SIGSPATIAL'16

SIGSPATIAL'16: 24th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems

October 31 - November 3, 2016

California, Burlingame

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SIGSPACIAL '16 Paper Acceptance Rate 40 of 216 submissions, 19%;

Overall Acceptance Rate 257 of 1,238 submissions, 21%

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Corcoran PJones C(2023)Topological data analysis for geographical information science using persistent homologyInternational Journal of Geographical Information Science10.1080/13658816.2022.215565437:3(712-745)Online publication date: 4-Jan-2023
https://doi.org/10.1080/13658816.2022.2155654
Corcoran PJones C(2021)A persistent homology model of street network connectivityTransactions in GIS10.1111/tgis.1284426:1(155-181)Online publication date: 27-Oct-2021
https://doi.org/10.1111/tgis.12844
Kim WMémoli F(2021)Generalized persistence diagrams for persistence modules over posetsJournal of Applied and Computational Topology10.1007/s41468-021-00075-1Online publication date: 5-Aug-2021
https://doi.org/10.1007/s41468-021-00075-1
Bubenik P(2020)The Persistence Landscape and Some of Its PropertiesTopological Data Analysis10.1007/978-3-030-43408-3_4(97-117)Online publication date: 26-Jun-2020
https://doi.org/10.1007/978-3-030-43408-3_4
Elchesen AMémoli F(2019)The reflection distance between zigzag persistence modulesJournal of Applied and Computational Topology10.1007/s41468-019-00031-0Online publication date: 27-Jul-2019
https://doi.org/10.1007/s41468-019-00031-0
Corcoran PJones CBanaei-Kashani FHoel EGüting RTamassia RXiong L(2018)Robust tracking of objects with dynamic topologyProceedings of the 26th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems10.1145/3274895.3274922(428-431)Online publication date: 6-Nov-2018
https://dl.acm.org/doi/10.1145/3274895.3274922
Corcoran PJones C(2018)Stability and Statistical Inferences in the Space of Topological Spatial RelationshipsIEEE Access10.1109/ACCESS.2018.28174936(18907-18919)Online publication date: 2018
https://doi.org/10.1109/ACCESS.2018.2817493
Corcoran PJones C(2017)Modelling Topological Features of Swarm Behaviour in Space and Time With Persistence LandscapesIEEE Access10.1109/ACCESS.2017.27493195(18534-18544)Online publication date: 2017
https://doi.org/10.1109/ACCESS.2017.2749319

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A reinforcement learning-based communication topology in particle swarm optimization

Optimization of the Distance Between Swarms Using Soft Computing

An Improved Particle Swarm Optimization Algorithm Based on Quotient Space Theory

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