Contemporary swarm indicators are often used in isolation, focussed on extracting information at the individual or collective levels. Consequently, these are seldom integrated to infer a top-level operating picture of the swarm, its members and its overall collective dynamics. The primary contribution of this paper is to organise a suite of indicators about swarms into an ontologically arranged collection of information markers to characterise the swarm from the perspective of an external observer – , a recognition agent. Our contribution shows the foundations for a new area of research that we title swarm analytics, whose primary concern is with the design and organisation of collections of swarm markers to understand, detect, recognise, track and learn a particular insight about a swarm system. We present our designed framework of information markers that offer a new avenue for swarm research, especially for heterogeneous and cognitive swarms that may require more advanced capabilities to detect agencies and categorise agent influences and responses.
AbbassH.HunjetR. (2021a). Smart shepherding: Towards transparent artificial intelligence enabled human-swarm teams. In Shepherding UxVs for human-swarm teaming: An artificial intelligence approach to unmanned X vehicles (pp. 1–28). Springer. https://doi.org/10.1007/978-3-030-60898-9_1
2.
AbbassH. A.HunjetR. A. (2021b). Shepherding UxVs for human-swarm teaming: An artificial intelligence approach to unmanned X vehicles. Springer.
3.
AlmeidaJ. P. A.CostaP. D.GuizzardiG. (2018). Towards an ontology of scenes and situations. In Conference on cognitive and computational aspects of situation management (CogSIMA) (pp. 29–35). IEEE. https://doi.org/10.1109/cogsima.2018.8423994
4.
AmornbunchornvejC. (2021). mFLICA: An r package for inferring leadership of coordination from time series. SoftwareX, 15, 100781. https://doi.org/10.1016/j.softx.2021.100781
5.
AndradeE.BlunsdenS.FisherR. (2006). Modelling crowd scenes for event detection. In 18th international conference on pattern recognition (ICPR’06) (Vol 1, pp. 175–178). ICPR.
6.
BaldiS.FrascaP. (2019). Adaptive synchronization of unknown heterogeneous agents: An adaptive virtual model reference approach. Journal of the Franklin Institute, 356(2), 935–955. https://doi.org/10.1016/j.jfranklin.2018.01.022
7.
BasakU. S. (2021). Study on identification of leader and follower agents and its interaction domain from trajectories in a collectively moving colony. PhD thesis. Hokkaido University
8.
BaumannM.BüningH. K. (2016). Learning shepherding behavior. PhD thesis. University of Paderborn.
9.
BaxterD. P.HepworthA. J.JoinerK. F.AbbassH. (2021). On the premise of a swarm guidance ontology for human-swarm teaming. In 65th annual meeting of the human factors and ergonomics society. Human Factors and Ergonomics Society.
10.
BossomaierT.BarnettL.HarréM.LizierJ. T. (2016). An introduction to transfer entropy: Information flow in complex systems. Springer International Publishing.
11.
BrownD.GoodrichM. (2014a). Limited bandwidth recognition of collective behavours in bio-inspired swarms. In Proceedings of the 13th international conference on autonomous agents and multiagent systems (AAMAS 2014). ACM.
12.
BrownD. S.GoodrichM. A. (2014b). Limited bandwidth recognition of collective behaviors in bio-inspired swarms. In Proceedings of the 2014 international Conference on autonomous Agents and multi-agent systems, AAMAS ’14 (pp. 405–412). International Foundation for Autonomous Agents and Multiagent Systems.
13.
ButailS.MwaffoV.PorfiriM. (2016). Model-free information-theoretic approach to infer leadership in pairs of zebrafish. Physical Review E, 93(4), 042411. https://doi.org/10.1103/PhysRevE.93.042411
14.
ChakrabortyD.BhuniaS.DeR. (2020). Survival chances of a prey swarm: How the cooperative interaction range affects the outcome. Scientific Reports, 10(1), 8362. https://doi.org/10.1038/s41598-020-64084-3
15.
CoftaP.LedzińskiD.ŚmigielS.GackowskaM. (2020). Cross-entropy as a metric for the robustness of drone swarms. Entropy, 22(6), 597. https://doi.org/10.3390/e22060597
16.
CrosatoE.JiangL.LechevalV.LizierJ. T.WangX. R.TichitP.TheraulazG.ProkopenkoM. (2018). Informative and misinformative interactions in a school of fish. Swarm Intell, 12(4), 283–305. https://doi.org/10.1007/s11721-018-0157-x
17.
DavisG. B. (2000). Information systems conceptual foundations: Looking backward and forward (pp. 61–82). Springer US
18.
DiukmanA. G. (2012). Swarm observations implementing integration theory to understand an opponent swarm. Master’s thesis. Naval Postgraduate School.
19.
DariT.GerdS.Tong-HunH.EffenbergA. O.PolaniD. (2020). Tilting together: An information-theoretic characterization of behavioral roles in rhythmic-dyadic interaction. Front. Hum. Neurosci, 14, 185. https://doi.org/10.3389/fnhum.2020.00185
20.
El-FiqiH.CampbellB.ElsayedS.PerryA.SinghH. K.HunjetR.AbbassH. A. (2020). The limits of reactive shepherding approaches for swarm guidance. IEEE Access, 8, 214658–214671. https://doi.org/10.1109/access.2020.3037325
21.
EmmanuelT.MaupongT.MpoelengD.SemongT.MphagoB.TabonaO. (2021). A survey on missing data in machine learning. Journal of Big Data, 8(1), 140. https://doi.org/10.1186/s40537-021-00516-9
22.
FerberJ. (1999). Multi-agent systems: An introduction to distributed artificial intelligence (1st ed.). Addison-Wesley Longman Publishing Co., Inc.
23.
Fernandez-RojasR.PerryA.SinghH.CampbellB.ElsayedS.HunjetR.AbbassH. A. (2019). Contextual awareness in human-advanced-vehicle systems: A survey. IEEE Access, 7(99), 33304–33328. https://doi.org/10.1109/access.2019.2902812
24.
GarlandJ.BerdahlA. M.SunJ.BolltE. M. (2018). Anatomy of leadership in collective behaviour. Chaos, 28(7), 075308. https://doi.org/10.1063/1.5024395
25.
GleissA.WilsonR.ShepardE. (2011). Making overall dynamic body acceleration work: On the theory of acceleration as a proxy for energy expenditure. Methods in Ecology and Evolution, 2(1), 23–33. https://doi.org/10.1111/j.2041-210x.2010.00057.x
26.
GongQ.KangW.WaltonC.KaminerI.ParkH. (2020). Partial observability analysis of an adversarial swarm model. Journal of Guidance, Control, and Dynamics, 43(2), 250–261. https://doi.org/10.2514/1.g004115
27.
HaeriH.JerathK.LeachmanJ. (2020). Thermodynamics-inspired macroscopic states of bounded swarms. ASME Letters in Dynamic Systems and Control, 1(1), 011015. https://doi.org/10.1115/1.4046580
28.
HamannH.SchmicklT.CrailsheimK. (2011). Explaining emergent behavior in a swarm system based on an inversion of the fluctuation theorem. In The 11th European conference on artificial life. ECAL.
29.
HasbachJ. D.BennewitzM. (2021). The design of self-organizing human–swarm intelligence. Adaptive Behavior, 30(4), 361–386. https://doi.org/10.1177/10597123211017550
30.
HauschildtV.GerkenM. (2016). Effect of pasture size on behavioural synchronization and spacing in German blackface ewes (ovis aries). Behavioural Processes, 124, 15–22. https://doi.org/10.1016/j.beproc.2015.12.001
31.
HepworthA. (2021). Activity recognition for shepherding. In AbbassH.HunjetR. (Eds.), Shepherding uxVs for human-swarm teaming chapter 7 (pp. 131–164). Springer.
32.
HepworthA. J.BaxterD. P.AbbassH. A. (2022). Onto4mat: A swarm shepherding ontology for generalized multiagent teaming. IEEE Access, 10, 59843–59861. https://doi.org/10.1109/access.2022.3180032
33.
HepworthA. J.BaxterD. P.HusseinA.YaxleyK. J.DebieE.AbbassH. A. (2021). Human-swarm-teaming transparency and trust architecture. IEEE/CAA J. Autom. Sinica, 8(7), 1281–1295. https://doi.org/10.1109/jas.2020.1003545
34.
HepworthA. J.YaxleyK. J.BaxterD. P.JoinerK. F.AbbassH. (2020). Tracking footprints in a swarm: Information-theoretic and spatial centre of influence measures. In Symposium series on computational intelligence (SSCI) (pp. 2217–2224). IEEE.
35.
HimoR.OguraM.OguraN.WakamiyaN. (2022). Iterative shepherding control for agents with heterogeneous responsivity. Mathematical Biosciences and Engineering, 19(4), 3509–3525. https://doi.org/10.3934/mbe.2022162
36.
HusseinA.PetrakiE.ElsawahS.AbbassH. (2022). Autonomous swarm shepherding using curriculum-based reinforcement learning. In FaliszewskiP.MascardiV.PelachaudC.TaylorM. (Eds.), Proc. Of the 21st international conference on autonomous agents and multiagent systems (AAMAS 2022). ACM.
37.
Jaén-VargasM.LeivaK. R.FernandesF.GoncalvesS. B.SilvaM. T.LopesD.OlmedoJ. S. (2022). Effects of sliding window variation in the performance of acceleration-based human activity recognition using deep learning models. Peer Journal of Computer Science, 8(e1052), 1–22. https://doi.org/10.7717/peerj-cs.1052
38.
JankovicL. (2018). Modelling computational fluid dynamics with swarm behaviour. In 4th building simulation and optimization conference (BSO) (pp. 112–118). IBPSA.
39.
KarakayaM.Maurizio PorfiriG. P (2020). Invasive alien species respond to biologically-inspired robotic predators. In Proc. SPIE 11374, bioinspiration, biomimetics, and bioreplication, X. SPIE.
40.
KathpaliaA. (2021). Theoretical and experimental investigations into causality, its measures and applications. National Institute of Advanced Studies.
41.
KengyelD.HamannH.ZahadatP.RadspielerG.WotawaF.SchmicklT. (2015). Potential of heterogeneity in collective behaviors: A case study on heterogeneous swarms. In International conference on principles and practice of multi-agent systems (pp. 201–217). Springer.
42.
KleanthousN.HussainA. J.KhanW.SneddonJ.Al-Shamma’aA.LiatsisP. (2022). A survey of machine learning approaches in animal behaviour. Neurocomputing, 491, 442–463. https://doi.org/10.1016/j.neucom.2021.10.126
LiL.MartinoliA.Abu-MostafaY. S. (2004). Learning and measuring specialization in collaborative swarm systems. Adaptive Behavior, 12(3–4), 199–212. https://doi.org/10.1177/105971230401200306
45.
LiM.HuZ.LiangJ.LiS. (2012). Shepherding behaviors with single shepherd in crowd management. In XiaoT.ZhangL.MaS. (Eds.), System simulation and scientific computing (pp. 415–423). Springer Berlin Heidelberg.
46.
LiuQ.HeM.XuD.DingN.WangY. (2018). A mechanism for recognizing and suppressing the emergent behavior of uav swarm. Mathematical Problems in Engineering, 2018(4), 1–14. https://doi.org/10.1155/2018/6734923
47.
LizierJ. T.ProkopenkoM.ZomayaA. Y. (2008). Local information transfer as a spatiotemporal filter for complex systems. Physical Review E, 77(2), 026110. https://doi.org/10.1103/PhysRevE.77.026110
48.
LongN. K.SammutK.SgariotoD.GarrattM.AbbassH. A. (2020). A comprehensive review of shepherding as a bio-inspired swarm-robotics guidance approach. IEEE Transactions on Emerging Topics in Computational Intelligence, 4(4), 523–537. https://doi.org/10.1109/tetci.2020.2992778
49.
LordW. M.SunJ.OuelletteN. T.BolltE. M. (2016). Inference of causal information flow in collective animal behavior. IEEE Transactions on Molecular, Biological and Multi-Scale Communications, 2(1), 107–116. https://doi.org/10.1109/tmbmc.2016.2632099
50.
Martín LópezL. M.Aguilar de SotoN.MadsenP. T.JohnsonM. (2022). Overall dynamic body acceleration measures activity differently on large versus small aquatic animals. Methods in Ecology and Evolution, 13(2), 447–458. https://doi.org/10.1111/2041-210X.13751
MillerJ. M.WangX. R.LizierJ. T.ProkopenkoM.RossiL. F. (2014). Measuring information dynamics in swarms (pp. 343–364). Springer Berlin Heidelberg.
57.
MiwaM.OishiK.NakagawaY.MaenoH.AnzaiH.KumagaiH.OkanoK.TobiokaH.HirookaH. (2015). Application of overall dynamic body acceleration as a proxy for estimating the energy expenditure of grazing farm animals: Relationship with heart rate. Plos One, 10(6), e0128042. https://doi.org/10.1371/journal.pone.0128042
58.
MocanuD. C.ExarchakosG.LiottaA. (2014). Node centrality awareness via swarming effects. In 2014 IEEE international conference on systems, man, and Cybernetics (SMC) (pp. 19–24). IEEE. https://doi.org/10.1109/smc.2014.6973878
59.
MohamedR. E.ElsayedS.HunjetR.AbbassH. (2021). A graph-based approach for shepherding swarms with limited sensing range. In 2021 congress on evolutionary computation (CEC) (pp. 2315–2322). IEEE. https://doi.org/10.1109/cec45853.2021.9504706
60.
MouldN.RegensJ. L.JensenC. J.IIIEdgerD. N. (2014). Video surveillance and counterterrorism: The application of suspicious activity recognition in visual surveillance systems to counterterrorism. Journal of Policing, Intelligence and Counter Terrorism, 9(2), 151–175. https://doi.org/10.1080/18335330.2014.940819
61.
NagarajN.BalasubramanianK.DeyS. (2013). A new complexity measure for time series analysis and classification. The European Physical Journal Special Topics, 222(3–4), 847–860. https://doi.org/10.1140/epjst/e2013-01888-9
62.
NguyenH. T.GarrattM.BuiL. T.AbbassH. (2020). Disturbances in influence of a shepherding agent is more impactful than sensorial noise during swarm guidance. In 2020 Symposium series on computational intelligence. IEEE.
63.
NovelliL.LizierJ. T. (2021). Inferring network properties from time series using transfer entropy and mutual information: Validation of multivariate versus bivariate approaches. Network Neuroscience, 5(2), 373–404. https://doi.org/10.1162/netn_a_00178
64.
NowakR.PorterR.BlacheD.DwyerC. (2008). Behaviour and the welfare of the sheep (pp. 81–134). Springer Netherlands.
65.
OrfandisS. J. (1988). Optimum signal processing: A n introduction (2nd ed.) University of Michigan: Macmillan.
66.
PapaspyrosV.BonnetF.CollignonB.MondadaF. (2019). Bidirectional interactions facilitate the integration of a robot into a shoal of zebrafish danio rerio. Plos One, 14(8), 25. https://doi.org/10.1371/journal.pone.0220559
67.
ParkH.GongQ.KangW.WaltonC.KaminerI. (2018). Observability analysis of an adversarial swarm’s cooperation strategy. In 14th international conference on control and automation (ICCA) (pp. 992–997). IEEE.
68.
PernekI.FerschaA. (2017). A survey of context recognition in surgery. Medical & Biological Engineering & Computing, 55(10), 1719–1734. https://doi.org/10.1007/s11517-017-1670-6
69.
PikovskyA.RosenblumM.KurthsJ. (2001). Synchronization: A universal concept in nonlinear sciences. In Cambridge nonlinear science series. Cambridge University Press.
70.
PilkiewiczK.LemassonBHRowlandMAHeinASunJBerdahlAMayoMLMoehlisJPorfiriMFernández-JuricicEGarnierSBolltEMCarlsonJMTarampiMRMacugaKLRossiLShenCC (2020). Decoding collective communications using information theory tools. J. R. Soc. Interface, 17(164), 20190563. https://doi.org/10.1098/rsif.2019.0563
71.
PorfiriM. (2018). Inferring causal relationships in zebrafish-robot interactions through transfer entropy: A small lure to catch a big fish. Animal Behavior and Cognition, 5(4), 341–367. https://doi.org/10.26451/abc.05.04.03.2018
72.
PriyadarshiniI.SharmaR.BhattD.Al-NumayM. (2022). Human activity recognition in cyber-physical systems using optimized machine learning techniques. Cluster Computing.
73.
PuckettJ. G.NiR.OuelletteN. T. (2015). Time-frequency analysis reveals pairwise interactions in insect swarms. Physical Review Letters, 114(25), 258103. https://doi.org/10.1103/PhysRevLett.114.258103
74.
QasemL.CardewA.WilsonA.GriffithsI.HalseyL. G.ShepardE. L. C.GleissA. C.WilsonR. (2012). Tri-axial dynamic acceleration as a proxy for animal energy expenditure; should we be summing values or calculating the vector?Plos One, 7(2), e31187. https://doi.org/10.1371/journal.pone.0031187
75.
Reséndiz-BenhumeaG. M.FroeseT.Ramos-FernándezG.Smith-AguilarS. E. (2019). Applying social network analysis to agent-based models: A case study of task allocation in swarm robotics inspired by ant foraging behavior. In Alife 2019: The 2019 conference on artificial life (pp. 616–623). ISAL.
76.
ReynoldsC. (1987). Flocks, herds and schools: A distributed behavioral model. In Proceedings of the 14th annual conference on computer graphics and interactive techniques of Siggraph ’87 (21, pp. 25–34). ACM.
77.
RezaeiA. A.MunozJ.JaliliM.KhayyamH. (2022). Vital node identification in complex networks using a machine learning-based approach. arXiv.
78.
SchaerfT. M.Herbert-ReadJ. E.WardA. J. W. (2021). A statistical method for identifying different rules of interaction between individuals in moving animal groups. Journal of the Royal Society Interface, 18(176), 20200925. https://doi.org/10.1098/rsif.2020.0925
ShangY.BouffanaisR. (2014). Influence of the number of topologically interacting neighbors on swarm dynamics. Scientific Reports, 4, 04184. https://doi.org/10.1038/srep04184
81.
SheikholeslamiS. (2019). Ablation programming for machine learning. Master’s thesis, KTH, School of Electrical Engineering and Computer Science (EECS).
82.
SipahiR.PorfiriM. (2020). Improving on transfer-entropy network reconstruction using time-delays: Approach and validation. Chaos, 30(2), 023125. https://doi.org/10.1063/1.5115510
83.
SpinelloCYangY.MacriP.PorfiriM. (2019). Zebrafish adjust their behavior in response to an interactive robotic predator. Frontiers in Robotics and AI, 6, 38. https://doi.org/10.3389/frobt.2019.00038
84.
StoicaP.RandolphM. (2005). Spectral analysis of signals. Prentice-Hall.
85.
StrömbomD.MannR. P.WilsonA. M.HailesS.MortonA. J.SumpterD. J. T.KingA. J. (2014). Solving the shepherding problem: Heuristics for herding autonomous, interacting agents. Journal of the Royal Society Interface, 11(100), 20140719. https://doi.org/10.1098/rsif.2014.0719
86.
SurasingheS.BolltE. M. (2020). On geometry of information flow for causal inference. Entropy, 22(4). https://doi.org/10.3390/e22040396
87.
SzwaykowskaK.RomeroL. M.-y.-T.SchwartzI. B. (2015). Collective motions of heterogeneous swarms. IEEE Transactions on Automation Science and Engineering, 12(3), 810–818. https://doi.org/10.1109/tase.2015.2403253
88.
TraboulsiA.BarbeauM. (2019). Recognition of drone formation intentions using supervised machine learning. In International conference on computational science and computational intelligence (CSCI) (pp. 408–411). IEEE.
89.
ValentiniG. (2019a). Revealing the structure of information flows discriminates similar animal social behaviors. bioRxiv preprint.
90.
ValentiniG.MizumotoN.PrattS.PavlicT.WalkerS. (2019b). Ants acknowledge information to control its rate of transfer. bioRxiv.
91.
WangX. R.MillerJ. M.LizierJ. T.ProkopenkoM.RossiL. F. (2011). Measuring information storage and transfer in swarms. In Eleventh European conference on the synthesis and simulation of living systems (pp. 838–845). ECAL.
92.
WangX. R.MillerJ. M.LizierJ. T.ProkopenkoM.RossiL. F. (2012). Quantifying and tracing information cascades in swarms. Plos One, 7(7), 1–7. https://doi.org/10.1371/journal.pone.0040084
93.
WilliamsT. (2007). Working sheep dogs: A practical guide to breeding, training and handling. Landlinks Press.
94.
WuY.SuJ.TangH.TianfieldH. (2011). Analysis of the emergence in swarm model based on largest lyapunov exponent. Mathematical Problems in Engineering, 2011(1024–123X). https://doi.org/10.1155/2011/745257
95.
YaxleyK.McIntyreN.ParkJ.HealeyJ. (2021a). Sky shepherds: A tale of a uav and sheep. In AbbassH.HunjetR. (Eds.), Shepherding uxVs for human-swarm teaming chapter 9 (pp. 189–206). Springer.
96.
YaxleyK. J.JoinerK. F.AbbassH. (2021b). Drone approach parameters leading to lower stress sheep flocking and movement: Sky shepherding. Scientific Reports, 11(1), 1–9. https://doi.org/10.1038/s41598-021-87453-y
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
