M^{-2}$ that is six orders of magnitude larger. When combined with constraints
from the measurement of gravitational waves from coalescing black-hole
binaries with LIGO/Virgo, these results show a striking validation of the
predictions of GR over a vast range of scales, from stellar mass black holes
to supermassive black holes that are billions of times larger.

##  8 Conclusion and Outlook

Here we present the results of 2017 EHT observations of Sgr A∗, the central
supermassive black hole in the Milky Way. We find evidence for intraday
structural variability in Sgr A∗, confirming changes that were hinted at in
prior observations across the electromagnetic spectrum. These variations
challenge standard approaches to interferometric analysis, so we have
developed a variety of methods to infer the structure of this source from our
data. From observations on April 7, on which we have the best-sampled data,
our analyses consistently reveal a ring-like structure, similar to that seen
in M87∗. Less complete observations on April 6 support this picture.

This ring of emission and its central brightness depression closely mirror the
structure expected from the plasma in accretion and outflow structures
bordering the event horizon of a black hole and partially lensed by its
gravity. The angular diameter of this ring is consistent with that expected
from the black hole mass inferred from stellar orbits. This consistency allows
us to restrict the allowed values of parameters that describe deviations from
a Kerr black hole, as predicted by General Relativity. We compare our data,
including measurements at other wavelengths, with a large suite of GRMHD
simulations. These simulations are remarkably successful at predicting the 1.3
mm image structure and broadband spectrum of Sgr A∗. However, the GRMHD
simulations tend to be more variable than the observations, which may be
related to our fluid modeling of a collisionless plasma or our neglect of
radiative cooling, and only a few configurations can satisfy our full set of
observational constraints apart from variability. Our results generally favor
models with dynamically strong magnetic fields, moderate (prograde) spin, a
lower inclination viewing angle, and strongly decoupled protons and electrons
in the emission region. Interestingly, these models also predict a reasonably
efficient (compared to the accretion rate) jet outflow, which points to
interesting complementary future studies. However more work is needed to fully
explore the physical parameter space, and to understand the variability.

As the nearest supermassive black hole, Sgr A∗ can be scrutinized in ways that
are impossible for other sources, making it a unique laboratory for exploring
the astrophysics of black holes and testing the predictions of General
Relativity. The results presented in these papers are the first EHT
contributions to the study of this source, but they are not the last.
Subsequent work will characterize the magnetic field configuration of this
source through polarimetric observations, as was done for M87∗, and describe
the structural changes associated with flare activity on April 11. Since 2017,
the EHT has continued to gather data using an increasing number of array
elements and doubled recording bandwidth. These data will provide improved
sensitivity and enable more robust imaging of this dynamic source, eventually
allowing movie reconstructions of plasma motions on the $\sim$hour orbital
timescales.

We thank the anonymous referees for helpful comments that improved the paper.
The Event Horizon Telescope Collaboration thanks the following organizations
and programs: the Academia Sinica; the Academy of Finland (projects 274477,
284495, 312496, 315721); the Agencia Nacional de Investigación y Desarrollo
(ANID), Chile via NCN$19\\_058$ (TITANs) and Fondecyt 1221421, the Alexander
von Humboldt Stiftung; an Alfred P. Sloan Research Fellowship; Allegro, the
European ALMA Regional Centre node in the Netherlands, the NL astronomy
research network NOVA and the astronomy institutes of the University of
Amsterdam, Leiden University and Radboud University; the ALMA North America
Development Fund; the Black Hole Initiative, which is funded by grants from
the John Templeton Foundation and the Gordon and Betty Moore Foundation
(although the opinions expressed in this work are those of the author(s) and
do not necessarily reflect the views of these Foundations); Chandra DD7-18089X
and TM6-17006X; the China Scholarship Council; China Postdoctoral Science
Foundation fellowship (2020M671266); Consejo Nacional de Ciencia y Tecnología
(CONACYT, Mexico, projects U0004-246083, U0004-259839, F0003-272050,
M0037-279006, F0003-281692, 104497, 275201, 263356); the Consejería de
Economía, Conocimiento, Empresas y Universidad of the Junta de Andalucía
(grant P18-FR-1769), the Consejo Superior de Investigaciones Científicas
(grant 2019AEP112); the Delaney Family via the Delaney Family John A. Wheeler
Chair at Perimeter Institute; Dirección General de Asuntos del Personal
Académico-Universidad Nacional Autónoma de México (DGAPA-UNAM, projects
IN112417 and IN112820); the Dutch Organization for Scientific Research (NWO)
VICI award (grant 639.043.513) and grant OCENW.KLEIN.113; the Dutch National
Supercomputers, Cartesius and Snellius (NWO Grant 2021.013); the EACOA
Fellowship awarded by the East Asia Core Observatories Association, which
consists of the Academia Sinica Institute of Astronomy and Astrophysics, the
National Astronomical Observatory of Japan, Center for Astronomical Mega-
Science, Chinese Academy of Sciences, and the Korea Astronomy and Space
Science Institute; the European Research Council (ERC) Synergy Grant
“BlackHoleCam: Imaging the Event Horizon of Black Holes" (grant 610058); the
European Union Horizon 2020 research and innovation programme under grant
agreements RadioNet (No 730562) and M2FINDERS (No 101018682); the Generalitat
Valenciana postdoctoral grant APOSTD/2018/177 and GenT Program (project
CIDEGENT/2018/021); MICINN Research Project PID2019-108995GB-C22; the European
Research Council for advanced grant ‘JETSET: Launching, propagation and
emission of relativistic jets from binary mergers and across mass scales’
(Grant No. 884631); the Institute for Advanced Study; the Istituto Nazionale
di Fisica Nucleare (INFN) sezione di Napoli, iniziative specifiche TEONGRAV;
the International Max Planck Research School for Astronomy and Astrophysics at
the Universities of Bonn and Cologne; DFG research grant “Jet physics on
horizon scales and beyond” (Grant No. FR 4069/2-1); Joint Princeton/Flatiron
and Joint Columbia/Flatiron Postdoctoral Fellowships, research at the Flatiron
Institute is supported by the Simons Foundation; the Japan Ministry of
Education, Culture, Sports, Science and Technology (MEXT; grant
JPMXP1020200109); the Japanese Government (Monbukagakusho: MEXT) Scholarship;
the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for JSPS
Research Fellowship (JP17J08829); the Joint Institute for Computational
Fundamental Science, Japan; the Key Research Program of Frontier Sciences,
Chinese Academy of Sciences (CAS, grants QYZDJ-SSW-SLH057, QYZDJSSW-SYS008,
ZDBS-LY-SLH011); the Leverhulme Trust Early Career Research Fellowship; the
Max-Planck-Gesellschaft (MPG); the Max Planck Partner Group of the MPG and the
CAS; the MEXT/JSPS KAKENHI (grants 18KK0090, JP21H01137, JP18H03721,
JP18K13594, 18K03709, JP19K14761, 18H01245, 25120007); the Malaysian
Fundamental Research Grant Scheme (FRGS) FRGS/1/2019/STG02/UM/02/6; the MIT
International Science and Technology Initiatives (MISTI) Funds; the Ministry
of Science and Technology (MOST) of Taiwan (103-2119-M-001-010-MY2,
105-2112-M-001-025-MY3, 105-2119-M-001-042, 106-2112-M-001-011,
106-2119-M-001-013, 106-2119-M-001-027, 106-2923-M-001-005,
107-2119-M-001-017, 107-2119-M-001-020, 107-2119-M-001-041,
107-2119-M-110-005, 107-2923-M-001-009, 108-2112-M-001-048,
108-2112-M-001-051, 108-2923-M-001-002, 109-2112-M-001-025,
109-2124-M-001-005, 109-2923-M-001-001, 110-2112-M-003-007-MY2,
110-2112-M-001-033, 110-2124-M-001-007, and 110-2923-M-001-001); the Ministry
of Education (MoE) of Taiwan Yushan Young Scholar Program; the Physics
Division, National Center for Theoretical Sciences of Taiwan; the National
Aeronautics and Space Administration (NASA, Fermi Guest Investigator grant
80NSSC20K1567, NASA Astrophysics Theory Program grant 80NSSC20K0527, NASA
NuSTAR award 80NSSC20K0645); NASA Hubble Fellowship grant HST-HF2-51431.001-A
awarded by the Space Telescope Science Institute, which is operated by the
Association of Universities for Research in Astronomy, Inc., for NASA, under
contract NAS5-26555; the National Institute of Natural Sciences (NINS) of
Japan; the National Key Research and Development Program of China (grant
2016YFA0400704, 2017YFA0402703, 2016YFA0400702); the National Science
Foundation (NSF, grants AST-0096454, AST-0352953, AST-0521233, AST-0705062,
AST-0905844, AST-0922984, AST-1126433, AST-1140030, DGE-1144085, AST-1207704,
AST-1207730, AST-1207752, MRI-1228509, OPP-1248097, AST-1310896, AST-1440254,
AST-1555365, AST-1614868, AST-1615796, AST-1715061, AST-1716327, AST-1716536,
OISE-1743747, AST-1816420, AST-1935980, AST-2034306); NSF Astronomy and
Astrophysics Postdoctoral Fellowship (AST-1903847); the Natural Science
Foundation of China (grants 11650110427, 10625314, 11721303, 11725312,
11873028, 11933007, 11991052, 11991053, 12192220, 12192223); the Natural
Sciences and Engineering Research Council of Canada (NSERC, including a
Discovery Grant and the NSERC Alexander Graham Bell Canada Graduate
Scholarships-Doctoral Program); the National Youth Thousand Talents Program of
China; the National Research Foundation of Korea (the Global PhD Fellowship
Grant: grants NRF-2015H1A2A1033752, the Korea Research Fellowship Program:
NRF-2015H1D3A1066561, Brain Pool Program: 2019H1D3A1A01102564, Basic Research
Support Grant 2019R1F1A1059721, 2021R1A6A3A01086420, 2022R1C1C1005255);
Netherlands Research School for Astronomy (NOVA) Virtual Institute of
Accretion (VIA) postdoctoral fellowships; Onsala Space Observatory (OSO)
national infrastructure, for the provisioning of its facilities/observational
support (OSO receives funding through the Swedish Research Council under grant
2017-00648); the Perimeter Institute for Theoretical Physics (research at
Perimeter Institute is supported by the Government of Canada through the
Department of Innovation, Science and Economic Development and by the Province
of Ontario through the Ministry of Research, Innovation and Science); the
Spanish Ministerio de Ciencia e Innovación (grants PGC2018-098915-B-C21,
AYA2016-80889-P, PID2019-108995GB-C21, PID2020-117404GB-C21); the University
of Pretoria for financial aid in the provision of the new Cluster Server nodes
and SuperMicro (USA) for a SEEDING GRANT approved towards these nodes in 2020;
the Shanghai Pilot Program for Basic Research, Chinese Academy of Science,
Shanghai Branch (JCYJ-SHFY-2021-013); the State Agency for Research of the
Spanish MCIU through the “Center of Excellence Severo Ochoa” award for the
Instituto de Astrofísica de Andalucía (SEV-2017- 0709); the Spinoza Prize SPI
78-409; the South African Research Chairs Initiative, through the South
African Radio Astronomy Observatory (SARAO, grant ID 77948), which is a
facility of the National Research Foundation (NRF), an agency of the
Department of Science and Innovation (DSI) of South Africa; the Toray Science
Foundation; Swedish Research Council (VR); the US Department of Energy (USDOE)
through the Los Alamos National Laboratory (operated by Triad National
Security, LLC, for the National Nuclear Security Administration of the USDOE
(Contract 89233218CNA000001); and the YCAA Prize Postdoctoral Fellowship.

We thank the staff at the participating observatories, correlation centers,
and institutions for their enthusiastic support. This paper makes use of the
following ALMA data: ADS/JAO.ALMA#2016.1.01154.V. ALMA is a partnership of the
European Southern Observatory (ESO; Europe, representing its member states),
NSF, and National Institutes of Natural Sciences of Japan, together with
National Research Council (Canada), Ministry of Science and Technology (MOST;
Taiwan), Academia Sinica Institute of Astronomy and Astrophysics (ASIAA;
Taiwan), and Korea Astronomy and Space Science Institute (KASI; Republic of
Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory
is operated by ESO, Associated Universities, Inc. (AUI)/NRAO, and the National
Astronomical Observatory of Japan (NAOJ). The NRAO is a facility of the NSF
operated under cooperative agreement by AUI. This research used resources of
the Oak Ridge Leadership Computing Facility at the Oak Ridge National
Laboratory, which is supported by the Office of Science of the U.S. Department
of Energy under Contract No. DE-AC05-00OR22725. We also thank the Center for
Computational Astrophysics, National Astronomical Observatory of Japan. The
computing cluster of Shanghai VLBI correlator supported by the Special Fund
for Astronomy from the Ministry of Finance in China is acknowledged.

APEX is a collaboration between the Max-Planck-Institut für Radioastronomie
(Germany), ESO, and the Onsala Space Observatory (Sweden). The SMA is a joint
project between the SAO and ASIAA and is funded by the Smithsonian Institution
and the Academia Sinica. The JCMT is operated by the East Asian Observatory on
behalf of the NAOJ, ASIAA, and KASI, as well as the Ministry of Finance of
China, Chinese Academy of Sciences, and the National Key Research and
Development Program (No. 2017YFA0402700) of China and Natural Science
Foundation of China grant 11873028. Additional funding support for the JCMT is
provided by the Science and Technologies Facility Council (UK) and
participating universities in the UK and Canada. The LMT is a project operated
by the Instituto Nacional de Astrófisica, Óptica, y Electrónica (Mexico) and
the University of Massachusetts at Amherst (USA). The IRAM 30-m telescope on
Pico Veleta, Spain is operated by IRAM and supported by CNRS (Centre National
de la Recherche Scientifique, France), MPG (Max-Planck-Gesellschaft, Germany)
and IGN (Instituto Geográfico Nacional, Spain). The SMT is operated by the
Arizona Radio Observatory, a part of the Steward Observatory of the University
of Arizona, with financial support of operations from the State of Arizona and
financial support for instrumentation development from the NSF. Support for
SPT participation in the EHT is provided by the National Science Foundation
through award OPP-1852617 to the University of Chicago. Partial support is
also provided by the Kavli Institute of Cosmological Physics at the University
of Chicago. The SPT hydrogen maser was provided on loan from the GLT, courtesy
of ASIAA.

This work used the Extreme Science and Engineering Discovery Environment
(XSEDE), supported by NSF grant ACI-1548562, and CyVerse, supported by NSF
grants DBI-0735191, DBI-1265383, and DBI-1743442. XSEDE Stampede2 resource at
TACC was allocated through TG-AST170024 and TG-AST080026N. XSEDE JetStream
resource at PTI and TACC was allocated through AST170028. This research is
part of the Frontera computing project at the Texas Advanced Computing Center
through the Frontera Large-Scale Community Partnerships allocation AST20023.
Frontera is made possible by National Science Foundation award OAC-1818253.
This research was carried out using resources provided by the Open Science
Grid, which is supported by the National Science Foundation and the U.S.
Department of Energy Office of Science. Additional work used ABACUS2.0, which
is part of the eScience center at Southern Denmark University. Simulations
were also performed on the SuperMUC cluster at the LRZ in Garching, on the
LOEWE cluster in CSC in Frankfurt, on the HazelHen cluster at the HLRS in
Stuttgart, and on the Pi2.0 and Siyuan Mark-I at Shanghai Jiao Tong
University. The computer resources of the Finnish IT Center for Science (CSC)
and the Finnish Computing Competence Infrastructure (FCCI) project are
acknowledged. This research was enabled in part by support provided by Compute
Ontario (http://computeontario.ca), Calcul Quebec (http://www.calculquebec.ca)
and Compute Canada (http://www.computecanada.ca).

The EHTC has received generous donations of FPGA chips from Xilinx Inc., under
the Xilinx University Program. The EHTC has benefited from technology shared
under open-source license by the Collaboration for Astronomy Signal Processing
and Electronics Research (CASPER). The EHT project is grateful to T4Science
and Microsemi for their assistance with Hydrogen Masers. This research has
made use of NASA’s Astrophysics Data System. We gratefully acknowledge the
support provided by the extended staff of the ALMA, both from the inception of
the ALMA Phasing Project through the observational campaigns of 2017 and 2018.
We would like to thank A. Deller and W. Brisken for EHT-specific support with
the use of DiFX. We thank Martin Shepherd for the addition of extra features
in the Difmap software that were used for the CLEAN imaging results presented
in this paper. We acknowledge the significance that Maunakea, where the SMA
and JCMT EHT stations are located, has for the indigenous Hawaiian people.

EHT, ALMA, APEX, IRAM:30m, JCMT, LMT, SMA, ARO:SMT, SPT, Chandra, EAVN, GMVA,
NuSTAR, Swift, VLT.

## References

  * Abbott et al. (2016) Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2016, Phys. Rev. Lett., 116, 061102, doi: 10.1103/PhysRevLett.116.061102
  * Agol (2000) Agol, E. 2000, ApJ, 538, L121, doi: 10.1086/312818
  * Baganoff et al. (2001) Baganoff, F. K., Bautz, M. W., Brandt, W. N., et al. 2001, Nature, 413, 45, doi: 10.1038/35092510
  * Baganoff et al. (2003) Baganoff, F. K., Maeda, Y., Morris, M., et al. 2003, ApJ, 591, 891, doi: 10.1086/375145
  * Balick & Brown (1974) Balick, B., & Brown, R. L. 1974, ApJ, 194, 265, doi: 10.1086/153242
  * Bardeen (1973) Bardeen, J. M. 1973, Les Astres Occlus, 215
  * Blackburn et al. (2019) Blackburn, L., Chan, C.-k., Crew, G. B., et al. 2019, ApJ, 882, 23, doi: 10.3847/1538-4357/ab328d
  * Blandford & Begelman (1999) Blandford, R. D., & Begelman, M. C. 1999, MNRAS, 303, L1, doi: 10.1046/j.1365-8711.1999.02358.x
  * Blandford & Königl (1979) Blandford, R. D., & Königl, A. 1979, ApJ, 232, 34, doi: 10.1086/157262
  * Bolton (1972) Bolton, C. T. 1972, Nature, 235, 271, doi: 10.1038/235271b0
  * Bower et al. (1999) Bower, G. C., Backer, D. C., Zhao, J.-H., Goss, M., & Falcke, H. 1999, ApJ, 521, 582, doi: 10.1086/307592
  * Bower et al. (2004) Bower, G. C., Falcke, H., Herrnstein, R. M., et al. 2004, Science, 304, 704, doi: 10.1126/science.1094023
  * Bower et al. (2006) Bower, G. C., Goss, W. M., Falcke, H., Backer, D. C., & Lithwick, Y. 2006, ApJ, 648, L127, doi: 10.1086/508019
  * Bower et al. (2003) Bower, G. C., Wright, M. C. H., Falcke, H., & Backer, D. C. 2003, ApJ, 588, 331
  * Broderick et al. (2009) Broderick, A. E., Fish, V. L., Doeleman, S. S., & Loeb, A. 2009, ApJ, 697, 45, doi: 10.1088/0004-637X/697/1/45
  * Broderick et al. (2022) Broderick, A. E., Gold, R., Georgiev, B., et al. 2022, in prep., 00, 0, doi: TBD
  * Broderick & Narayan (2006) Broderick, A. E., & Narayan, R. 2006, ApJ, 638, L21, doi: 10.1086/500930
  * Broderick et al. (2020) Broderick, A. E., Gold, R., Karami, M., et al. 2020, ApJ, 897, 139, doi: 10.3847/1538-4357/ab91a4
  * Chan et al. (2015) Chan, C.-K., Psaltis, D., Özel, F., Narayan, R., & Saḑowski, A. 2015, ApJ, 799, 1, doi: 10.1088/0004-637X/799/1/1
  * Chatterjee et al. (2020) Chatterjee, K., Younsi, Z., Liska, M., et al. 2020, MNRAS, 499, 362, doi: 10.1093/mnras/staa2718
  * Coker et al. (1999) Coker, R., Melia, F., & Falcke, H. 1999, ApJ, 523, 642, doi: 10.1086/307770
  * Dexter et al. (2009) Dexter, J., Agol, E., & Fragile, P. C. 2009, ApJ, 703, L142, doi: 10.1088/0004-637X/703/2/L142
  * Do et al. (2019) Do, T., Hees, A., Ghez, A., et al. 2019, Science, 365, 664, doi: 10.1126/science.aav8137
  * Doeleman et al. (2001) Doeleman, S. S., Shen, Z.-Q., Rogers, A. E. E., et al. 2001, AJ, 121, 2610, doi: 10.1086/320376
  * Doeleman et al. (2008) Doeleman, S. S., Weintroub, J., Rogers, A. E. E., et al. 2008, Nature, 455, 78, doi: 10.1038/nature07245
  * Eckart et al. (2004) Eckart, A., Baganoff, F. K., Morris, M., et al. 2004, A&A, 427, 1, doi: 10.1051/0004-6361:20040495
  * EHT MWL Science Working Group et al. (2021) EHT MWL Science Working Group, Algaba, J. C., Anczarski, J., et al. 2021, ApJ, 911, L11, doi: 10.3847/2041-8213/abef71
  * Einstein (1915) Einstein, A. 1915, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften (Berlin), 844
  * Ekers et al. (1975) Ekers, R. D., Goss, W. M., Schwarz, U. J., Downes, D., & Rogstad, D. H. 1975, A&A, 43, 159
  * Event Horizon Telescope Collaboration et al. (2019a) Event Horizon Telescope Collaboration, Akiyama, K., Alberdi, A., et al. 2019a, ApJ, 875, L1, doi: 10.3847/2041-8213/ab0ec7
  * Event Horizon Telescope Collaboration et al. (2019b) —. 2019b, ApJ, 875, L2, doi: 10.3847/2041-8213/ab0c96
  * Event Horizon Telescope Collaboration et al. (2019c) —. 2019c, ApJ, 875, L3, doi: 10.3847/2041-8213/ab0c57
  * Event Horizon Telescope Collaboration et al. (2019d) —. 2019d, ApJ, 875, L4, doi: 10.3847/2041-8213/ab0e85
  * Event Horizon Telescope Collaboration et al. (2019e) —. 2019e, ApJ, 875, L5, doi: 10.3847/2041-8213/ab0f43
  * Event Horizon Telescope Collaboration et al. (2019f) —. 2019f, ApJ, 875, L6, doi: 10.3847/2041-8213/ab1141
  * Event Horizon Telescope Collaboration et al. (2021a) —. 2021a, ApJ, 875, L7
  * Event Horizon Telescope Collaboration et al. (2021b) —. 2021b, ApJ, 875, L8
  * Event Horizon Telescope Collaboration et al. (2022a) —. 2022a, ApJ, 875, 2
  * Event Horizon Telescope Collaboration et al. (2022b) —. 2022b, ApJ, 875, 3
  * Event Horizon Telescope Collaboration et al. (2022c) —. 2022c, ApJ, 875, 4
  * Event Horizon Telescope Collaboration et al. (2022d) —. 2022d, ApJ, 875, 5
  * Event Horizon Telescope Collaboration et al. (2022e) —. 2022e, ApJ, 875, 6
  * Fabian (2012) Fabian, A. C. 2012, ARA&A, 50, 455, doi: 10.1146/annurev-astro-081811-125521
  * Falcke et al. (1998) Falcke, H., Goss, W. M., Matsuo, H., et al. 1998, ApJ, 499, 731, doi: 10.1086/305687
  * Falcke et al. (1993) Falcke, H., Mannheim, K., & Biermann, P. L. 1993, A&A, 278, L1.  https://arxiv.org/abs/astro-ph/9308031
  * Falcke et al. (2000) Falcke, H., Melia, F., & Agol, E. 2000, ApJ, 528, L13, doi: 10.1086/312423
  * Farah et al. (2022) Farah, J. R., et al. 2022, in prep., 00, 0, doi: TBD
  * Fish et al. (2011) Fish, V. L., Doeleman, S. S., Beaudoin, C., et al. 2011, ApJ, 727, L36, doi: 10.1088/2041-8205/727/2/L36
  * Gammie et al. (2003) Gammie, C. F., McKinney, J. C., & Tóth, G. 2003, ApJ, 589, 444, doi: 10.1086/374594
  * García et al. (1995) García, A., Galtsov, D., & Kechkin, O. 1995, Phys. Rev. Lett., 74, 1276, doi: 10.1103/PhysRevLett.74.1276
  * Genzel et al. (2003) Genzel, R., Schödel, R., Ott, T., et al. 2003, Nature, 425, 934, doi: 10.1038/nature02065
  * Georgiev et al. (2022) Georgiev, B., et al. 2022, in prep., 00, 0, doi: TBD
  * Ghez et al. (2003) Ghez, A. M., Duchêne, G., Matthews, K., et al. 2003, ApJ, 586, L127, doi: 10.1086/374804
  * Ghez et al. (2008) Ghez, A. M., Salim, S., Weinberg, N. N., et al. 2008, ApJ, 689, 1044, doi: 10.1086/592738
  * Gillessen et al. (2009) Gillessen, S., Eisenhauer, F., Fritz, T. K., et al. 2009, ApJ, 707, L114, doi: 10.1088/0004-637X/707/2/L114
  * Goldwurm et al. (1994) Goldwurm, A., Cordier, B., Paul, J., et al. 1994, Nature, 371, 589, doi: 10.1038/371589a0
  * Gravity Collaboration et al. (2018a) Gravity Collaboration, Abuter, R., Amorim, A., et al. 2018a, A&A, 615, L15, doi: 10.1051/0004-6361/201833718
  * Gravity Collaboration et al. (2018b) —. 2018b, A&A, 618, L10, doi: 10.1051/0004-6361/201834294
  * Gravity Collaboration et al. (2019) —. 2019, A&A, 625, L10, doi: 10.1051/0004-6361/201935656
  * Gravity Collaboration et al. (2022) Gravity Collaboration, Abuter, R., Aimar, N., et al. 2022, A&A, 657, L12, doi: 10.1051/0004-6361/202142465
  * Hilbert (1917) Hilbert, D. 1917, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen - Mathematisch-physikalische Klasse (Berlin: Weidmannsche Buchhandlung), 53–76
  * Ho (1999) Ho, L. C. 1999, ApJ, 516, 672, doi: 10.1086/307137
  * Janssen et al. (2019) Janssen, M., Goddi, C., van Bemmel, I. M., et al. 2019, A&A, 626, A75, doi: 10.1051/0004-6361/201935181
  * Jaroszynski & Kurpiewski (1997) Jaroszynski, M., & Kurpiewski, A. 1997, A&A, 326, 419.  https://arxiv.org/abs/astro-ph/9705044
  * Johannsen & Psaltis (2011) Johannsen, T., & Psaltis, D. 2011, Phys. Rev. D, 83, 124015, doi: 10.1103/PhysRevD.83.124015
  * Johnson et al. (2015) Johnson, M. D., Fish, V. L., Doeleman, S. S., et al. 2015, Science, 350, 1242, doi: 10.1126/science.aac7087
  * Johnson et al. (2018) Johnson, M. D., Narayan, R., Psaltis, D., et al. 2018, ApJ, 865, 104.  https://arxiv.org/abs/1808.08966
  * Joshi et al. (2014) Joshi, P. S., Malafarina, D., & Narayan, R. 2014, Classical and Quantum Gravity, 31, 015002, doi: 10.1088/0264-9381/31/1/015002
  * Kerr (1963) Kerr, R. P. 1963, Phys. Rev. Lett., 11, 237, doi: 10.1103/PhysRevLett.11.237
  * Kormendy & Ho (2013) Kormendy, J., & Ho, L. C. 2013, ARA&A, 51, 511, doi: 10.1146/annurev-astro-082708-101811
  * Krichbaum et al. (1998) Krichbaum, T. P., Graham, D. A., Witzel, A., et al. 1998, A&A, 335, L106
  * Lee & Gammie (2021) Lee, D., & Gammie, C. F. 2021, ApJ, 906, 39, doi: 10.3847/1538-4357/abc8f3
  * Liska et al. (2018) Liska, M., Hesp, C., Tchekhovskoy, A., et al. 2018, MNRAS, 474, L81, doi: 10.1093/mnrasl/slx174
  * Lo et al. (1975) Lo, K. Y., Schilizzi, R. T., Cohen, M. H., & Ross, H. N. 1975, ApJ, 202, L63, doi: 10.1086/181982
  * Lo et al. (1998) Lo, K. Y., Shen, Z.-Q., Zhao, J.-H., & Ho, P. T. P. 1998, ApJ, 508, L61, doi: 10.1086/311726
  * Lu et al. (2018) Lu, R.-S., Krichbaum, T. P., Roy, A. L., et al. 2018, ApJ, 859, 60, doi: 10.3847/1538-4357/aabe2e
  * Luminet (1979) Luminet, J.-P. 1979, A&A, 75, 228
  * Lynden-Bell (1969) Lynden-Bell, D. 1969, Nature, 223, 690, doi: 10.1038/223690a0
  * Magorrian et al. (1998) Magorrian, J., Tremaine, S., Richstone, D., et al. 1998, AJ, 115, 2285, doi: 10.1086/300353
  * Markoff et al. (2001) Markoff, S., Falcke, H., Yuan, F., & Biermann, P. L. 2001, A&A, 379, L13, doi: 10.1051/0004-6361:20011346
  * Marrone et al. (2007) Marrone, D. P., Moran, J. M., Zhao, J. ., & Rao, R. 2007, ApJ, 654, L57
  * Marrone et al. (2006) Marrone, D. P., Moran, J. M., Zhao, J.-H., & Rao, R. 2006, ApJ, 640, 308, doi: 10.1086/500106
  * McClintock & Remillard (1986) McClintock, J. E., & Remillard, R. A. 1986, ApJ, 308, 110, doi: 10.1086/164482
  * Mościbrodzka et al. (2016) Mościbrodzka, M., Falcke, H., & Shiokawa, H. 2016, A&A, 586, A38, doi: 10.1051/0004-6361/201526630
  * Mościbrodzka et al. (2009) Mościbrodzka, M., Gammie, C. F., Dolence, J. C., Shiokawa, H., & Leung, P. K. 2009, ApJ, 706, 497, doi: 10.1088/0004-637X/706/1/497
  * Nagar et al. (2000) Nagar, N. M., Falcke, H., Wilson, A. S., & Ho, L. C. 2000, ApJ, 542, 186, doi: 10.1086/309524
  * Narayan et al. (2000) Narayan, R., Igumenshchev, I. V., & Abramowicz, M. A. 2000, ApJ, 539, 798, doi: 10.1086/309268
  * Narayan et al. (2003) —. 2003, PASJ, 55, L69, doi: 10.1093/pasj/55.6.L69
  * Narayan & McClintock (2008) Narayan, R., & McClintock, J. E. 2008, New A Rev., 51, 733, doi: 10.1016/j.newar.2008.03.002
  * Narayan et al. (2012) Narayan, R., Sądowski, A., Penna, R. F., & Kulkarni, A. K. 2012, MNRAS, 426, 3241, doi: 10.1111/j.1365-2966.2012.22002.x
  * Narayan et al. (1995) Narayan, R., Yi, I., & Mahadevan, R. 1995, Nature, 374, 623, doi: 10.1038/374623a0
  * Olivares et al. (2020) Olivares, H., Younsi, Z., Fromm, C. M., et al. 2020, MNRAS, 497, 521, doi: 10.1093/mnras/staa1878
  * Oppenheimer & Snyder (1939) Oppenheimer, J. R., & Snyder, H. 1939, Physical Review, 56, 455, doi: 10.1103/PhysRev.56.455
  * Özel et al. (2000) Özel, F., Psaltis, D., & Narayan, R. 2000, ApJ, 541, 234, doi: 10.1086/309396
  * Özel et al. (2021) Özel, F., Psaltis, D., & Younsi, Z. 2021, arXiv e-prints, arXiv:2111.01123.  https://arxiv.org/abs/2111.01123
  * Padin et al. (1990) Padin, S., Woody, D. P., Hodges, M. W., et al. 1990, ApJ, 360, L11, doi: 10.1086/185800
  * Penrose (1965) Penrose, R. 1965, Phys. Rev. Lett., 14, 57, doi: 10.1103/PhysRevLett.14.57
  * Predehl & Truemper (1994) Predehl, P., & Truemper, J. 1994, A&A, 290, L29
  * Psaltis et al. (2018) Psaltis, D., Johnson, M., Narayan, R., et al. 2018, ArXiv e-prints.  https://arxiv.org/abs/1805.01242
  * Psaltis et al. (2020) Psaltis, D., Medeiros, L., Christian, P., et al. 2020, Phys. Rev. Lett., 125, 141104, doi: 10.1103/PhysRevLett.125.141104
  * Quataert (2002) Quataert, E. 2002, ApJ, 575, 855, doi: 10.1086/341425
  * Quataert & Gruzinov (2000a) Quataert, E., & Gruzinov, A. 2000a, ApJ, 539, 809, doi: 10.1086/309267
  * Quataert & Gruzinov (2000b) —. 2000b, ApJ, 545, 842, doi: 10.1086/317845
  * Reid & Brunthaler (2020) Reid, M. J., & Brunthaler, A. 2020, ApJ, 892, 39, doi: 10.3847/1538-4357/ab76cd
  * Reid et al. (2019) Reid, M. J., Menten, K. M., Brunthaler, A., et al. 2019, ApJ, 885, 131, doi: 10.3847/1538-4357/ab4a11
  * Ressler et al. (2020) Ressler, S. M., White, C. J., Quataert, E., & Stone, J. M. 2020, ApJ, 896, L6, doi: 10.3847/2041-8213/ab9532
  * Richstone et al. (1998) Richstone, D., Ajhar, E. A., Bender, R., et al. 1998, Nature, 385, A14.  https://arxiv.org/abs/astro-ph/9810378
  * Rogers et al. (1994) Rogers, A. E. E., Doeleman, S., Wright, M. C. H., et al. 1994, ApJ, 434, L59, doi: 10.1086/187574
  * Russell et al. (2017) Russell, C. M. P., Wang, Q. D., & Cuadra, J. 2017, MNRAS, 464, 4958, doi: 10.1093/mnras/stw2584
  * Satapathy et al. (2022) Satapathy, K., Psaltis, D., Özel, F., et al. 2022, ApJ, 925, 13, doi: 10.3847/1538-4357/ac332e
  * Schmidt (1963) Schmidt, M. 1963, Nature, 197, 1040, doi: 10.1038/1971040a0
  * Schödel et al. (2002) Schödel, R., Ott, T., Genzel, R., et al. 2002, Nature, 419, 694, doi: 10.1038/nature01121
  * Schwarzschild (1916) Schwarzschild, K. 1916, Abh. Konigl. Preuss. Akad. Wissenschaften Jahre 1906,92, Berlin,1907, 1916, 189
  * Shaikh et al. (2019) Shaikh, R., Kocherlakota, P., Narayan, R., & Joshi, P. S. 2019, MNRAS, 482, 52, doi: 10.1093/mnras/sty2624
  * Shen et al. (2005) Shen, Z.-Q., Lo, K. Y., Liang, M.-C., Ho, P. T. P., & Zhao, J.-H. 2005, Nature, 438, 62, doi: 10.1038/nature04205
  * Thompson et al. (2017) Thompson, A. R., Moran, J. M., & Swenson, Jr., G. W. 2017, Interferometry and Synthesis in Radio Astronomy, 3rd Edition (Springer International Publishing), doi: 10.1007/978-3-319-44431-4
  * Wang et al. (2013) Wang, Q. D., Nowak, M. A., Markoff, S. B., et al. 2013, Science, 341, 981, doi: 10.1126/science.1240755
  * Webster & Murdin (1972) Webster, B. L., & Murdin, P. 1972, Nature, 235, 37, doi: 10.1038/235037a0
  * White & Quataert (2022) White, C. J., & Quataert, E. 2022, ApJ, 926, 136, doi: 10.3847/1538-4357/ac423c
  * Wielgus et al. (2022) Wielgus, M., Marchili, N., Martí-Vidal, I., et al. 2022, in prep., 00, 0, doi: TBD
  * Younsi et al. (2021) Younsi, Z., Psaltis, D., & Özel, F. 2021, arXiv e-prints, arXiv:2111.01752.  https://arxiv.org/abs/2111.01752
  * Yuan & Narayan (2014) Yuan, F., & Narayan, R. 2014, ARA&A, 52, 529, doi: 10.1146/annurev-astro-082812-141003
  * Zylka et al. (1992) Zylka, R., Mezger, P. G., & Lesch, H. 1992, A&A, 261, 119

  *[ALMA]: Atacama Large Millimeter/submillimeter Array
  *[APEX]: Atacama Pathfinder Experiment
  *[LMT]: Large Millimeter Telescope Alfonso Serrano
  *[JCMT]: James Clerk Maxwell Telescope
  *[SMA]: Submillimeter Array
  *[SMT]: Submillimeter Telescope
  *[SPT]: South Pole Telescope
  *[PV]: IRAM 30 m Telescope


11institutetext: School of Computer Science, College of Science
University College Dublin, Belfield, Dublin 4, Ireland
11email<EMAIL_ADDRESS>11email: {tahar.kechadi<EMAIL_ADDRESS>
# OAK: Ontology-based Knowledge Map
Model for Digital Agriculture

Quoc Hung Ngo  Tahar Kechadi  Nhien-An Le-Khac

###### Abstract

Nowadays, a huge amount of knowledge has been amassed in digital agriculture.
This knowledge and know-how information are collected from various sources,
hence the question is how to organise this knowledge so that it can be
efficiently exploited. Although this knowledge about agriculture practices can
be represented using ontology, rule-based expert systems, or knowledge model
built from data mining processes, the scalability still remains an open issue.
In this study, we propose a knowledge representation model, called an
ontology-based knowledge map, which can collect knowledge from different
sources, store it, and exploit either directly by stakeholders or as an input
to the knowledge discovery process (Data Mining). The proposed model consists
of two stages, 1) build an ontology as a knowledge base for a specific domain
and data mining concepts, and 2) build the ontology-based knowledge map model
for representing and storing the knowledge mined on the crop datasets. A
framework of the proposed model has been implemented in agriculture domain. It
is an efficient and scalable model, and it can be used as knowledge repository
a digital agriculture. .

###### Keywords:

Ontology Knowledge Map Knowledge Management Digital Agriculture

##  1 Introduction

The knowledge from crop studies is turned into profitable decisions in digital
farming only when it is efficiently managed. Farming knowledge can be created
by the experience of farmers, by research studies in agronomy, or by analyses
of data that has been collected for a number of years. In particular, the
knowledge discovery in agricultural data is one of the most diverse, large,
and dynamic in digital farming.

Moreover, one of the key challenges of knowledge management is the
representation of the mined results, which are not consistent among different
sources of knowledge. For example, consider two results that were obtained
from two data mining studies, with the overall goal of predicting farming
conditions of high crop yield of winter wheat. The concept high crop yield
used in the two studies can be different, depending on the way authors define
the range of high crop yield. Therefore, the overall insight may not be
consistent to be used in the same system or to compare those results. This
issue can also occur with input attributes used by different predictive
models. In addition, the farming knowledge represented using an ontology is
static and it is difficult to generalise to different regions, which have
different farming conditions. The knowledge represented as rules in expert
systems does not scale well and there is no way to refine the rules and it is
also very difficult to check the coherence of all rules within a system. To
summarise, while the knowledge mined from data mining processes is dynamic and
flexible but its representation differs from one process to another. Some
knowledge representation models are rules oriented while others are stored as
vectors or trained models.

In this paper, we propose a scalable ontology-based knowledge map (OAK) model
for representing, storing, managing and retrieving knowledge of any type. The
main contribution of the model is to support data scientists and agronomists
in managing and using mined knowledge for decision making with ease. The next
section gives an overview of knowledge concepts and how to create knowledge in
the agriculture domain. Section 3 describes in details the proposed OAK model,
which includes definitions, architecture and its three main modules. Section 4
provides various experiments on the knowledge management system, which is
based on OAK model. Finally, we conclude and give some future directions in
Section 5.

##  2 Related Work

According to the Collins
dictionary111https://www.collinsdictionary.com/dictionary/english/knowledge,
knowledge is an information and understanding about a subject, which a person
has, or which all people have, while the Cambridge dictionary defines the
knowledge as an information and understanding that you have in your mind.
Knowledge Map (KMap) is defined as a spacial representation of information
[22]. Knowledge maps are used extensively in enterprises to describe how, what
or where to find useful knowledge within the enterprise organisations [6].
Knowledge graph (KG) is a set of pairs of knowledge $(V,E)$, where $V$ is a
set of nodes mapped to pieces of knowledge in the domain and $E$ is a set of
knowledge relations between two nodes. Ontology is a formal specification of
the vocabulary to be used in specifying knowledge and the purpose of the
ontology is to provide a uniform text-based knowledge representation, which is
comprehensible by either human or machines [8]. The difference between these
three concepts (KMap, KG, and ontology) is that ontology is used for formal
and static knowledge, while KMaps and KG are used for handling more dynamic
knowledge types, such as enterprise KMaps or Google Knowledge
Graph222https://developers.google.com/knowledge-graph.

In the following, discuss some relevant knowledge discovery processes in
agriculture, particularly data mining, and review the knowledge representation
and management gaps as a consequence of proliferation of big data analytics.

###  2.1 Knowledge Discovery in Agriculture

There are many ways in creating knowledge in any specific domain. The first
method is to acquire knowledge manually by experts. The result of this
approach is knowledge-base (known as taxonomy or ontology), or rule-based
system (known as expert systems). Another way is to acquire knowledge
automatically via a knowledge discovery process from structured or
unstructured data. However, knowledge graphs are normally built from
Wikipedia, Freebase, DBpedia and agriculture websites, such as, the AgriKG [4]
and Cn-MAKG [5] systems.

During the last decade, the advances in digital agriculture have led to
numerous significant studies on the application of data mining process to
agricultural datasets. These datasets include including soil, weather, crop
yield, and disease prediction. Moreover, the scope of research for data mining
in agriculture is also diverse, including data construction as well as
forecasting models. In this context, there are several computational soil
studies, such as building datasets of soil profiles [21], monitoring soil
characteristics under effects of other factors and crop yield [3], or using
soil characteristics to predict other soil characteristics [23]. Another
common application of knowledge mining in agriculture is crop yield prediction
(e.g., predicting yield or wheat yield based on soil attributes, weather
factors, and management factors [1], [12], [18]). Finally, the third common
application of knowledge mining is the disease prediction or the protection
plan (e.g., detecting nitrogen stress in early crop growth stage of corn
fields [14], or detecting and classifying sugar beet diseases [7], etc.).

Data mining has four main categories of techniques; clustering,
classification, regression, and association rule. To date, only classification
and regression are widely used in digital agriculture. Usually, classification
approaches are used to detect the disease (mostly based on the images
processing techniques [7]), or to classify crop yield (as low, medium or high
yield). Regression techniques are mainly used to predict crop yields based on
different input attributes [1], [3]. Although the number of knowledge model
types is not large, input and output attributes for forecasting models are
totally different and diverse, and the number of agricultural attributes is
very large. In addition, the idea of using KMaps for handling mined knowledge
has been proposed in [9] and [10], however, it only proposed as a prototype
for handling rules in data mining result. Therefore, the challenge of these
knowledge types and KMaps approach for these knowledge types is that most of
them are stored as pre-trained models or as computer software and their final
results are mostly published as scientific papers or reports.

###  2.2 Methodology for Building Knowledge Map

There are many approaches for building knowledge maps (KMap). Most of these
methodologies were dedicated to enterprise KMaps while several others are used
to build specific domain of KMaps. For example, Bargent [2] proposed an
11-step methodology for building an enterprise KMap, which is a common
strategy of software development life-cycle. Similarly, Kim et al.[8] proposed
a 6-step methodology for capturing and representing organisational KMaps with
knowledge profiles and business processes, while Pei et al. [19] introduced a
7-step methodology to build an enterprise KMap for matrix organisations,
including setting up a development team, analysis knowledge resources,
definition of the business knowledge domain boundaries, determination of the
structure and relationship for the KMap, selection of the development tools,
identification of locations of knowledge items and drawing the initial KMap,
and finally evaluation and updates of KMap.

Moreover, several studies have used ontology for building their knowledge
maps. Lecocq [11] developed a 4-phase methodology with planning, collecting,
mapping and validating phases based on an ontology for visually representing
knowledge assets. In another study, Mansingh et al. [15] introduced a 3-stage
methodology for building KMaps of medical-care processes; including creation
of an ontology from the medical cases, creation of the process map with
flowcharts and petri nets, and extraction of KMaps from instances of different
medical-care processes (represented as medical files) by using vocabulary and
relationships in that ontology. The method was tested in a healthcare
organisation and was found to be suitable to build a KMap, which combines
conceptual and process maps for medical-care processes.

To summarise, existing methodologies for building KMaps can be divided into
two typical types; methods for building enterprise KMaps [2] [8] [13] [19] and
methods for building conceptual KMaps [11] [15]. For building enterprise
KMaps, although methodologies have different number of steps, they use basic
stages: (1) identify the scope, domain of KMap and the develop team, (2)
identify knowledge resources or materials, (3) identify knowledge in each
knowledge item, (4) extract and build KMap, (5) evaluate, use, and update the
KMap. For building conceptual KMaps or hybrid with conceptual maps, existing
methodologies also have the same basic stages, however, one step in
identifying knowledge resources or materials is to use an ontology as a
conceptual framework for building KMap in subsequent stages. This step aims to
locate the knowledge items in the final KMaps.

##  3 Ontology-based Knowledge Map Model

We propose an ontology-base knowledge map model for representing knowledge
obtained from learning processes applied to agricultural data, from research
articles, or from experts in the domain. Moreover, the model allows knowledge
handling and exploitation in a flexible and scalable way. As illuminated in an
example in Figure 1, the knowledge representation shows the results of a
clustering model with 5 input attributes (Soil pH, seed rate, nitrogen, wheat
name, and mean yield).

To implement the model and validate it experimentally, the system is designed
and developed in two major phases: during the first phase we build an
agriculture ontology and in the second phase we use the ontology vocabulary
along with initial data schema (as in the data warehouse) to model the
knowledge. Before going into the details, we need to define the key concepts
behind this model, which are knowledge representation, ontology, knowledge map
model, concept, transformation, instance, state, relation, lexicon and
hierarchy.

Figure 1: Approach for Knowledge Map Model for Clustering.

###### Definition 1

A Knowledge representation $\mathbb{K}$ is defined by a set of four elements,
containing instances $\mathbb{I}$, transformations $\mathbb{T}$, states
$\mathbb{S}$, and relations $\mathbb{R}$:

$\mathbb{K}=(\mathbb{I},\mathbb{T},\mathbb{S},\mathbb{R})$ (1)

###### Definition 2

An Ontology $\mathbb{O}$ is defined by a set of three elements, containing
concepts $\mathbb{C}$ , transformations $\mathbb{T}$, and relations
$\mathbb{R}$:

$\mathbb{O}=(\mathbb{C},\mathbb{T},\mathbb{R})$ (2)

###### Definition 3

A Knowledge Map Model $\mathbb{KM}$ is defined by a set containing five
elements, $\mathbb{C}$, $\mathbb{I}$, $\mathbb{T}$, $\mathbb{S}$, and
$\mathbb{R}$, which are corresponding sets of concept $c$, instance $i$,
transformation $t$, state $t$ and relation $r$.

$\mathbb{KM}=(\mathbb{C},\mathbb{I},\mathbb{T},\mathbb{S},\mathbb{R})$ (3)

Where $\mathbb{C}$ is a set of concepts $\\{c\\}$, and represents a set of
entities or attributes of an entity within a domain and four data mining
categories of results (clustering, classification, regression, and association
rule).

$\mathbb{T}$ is a set of transformations $\\{t\\}$, and represents a set of
functions $f(x)$ to transform the value of entities $x$ from value range
$\mathbb{R}_{x}$ to value range $\mathbb{R}_{y}$.

$\mathbb{I}$ is a set of instances $\\{i\\}$, and represents a set of
entities.

$\mathbb{S}$ is a set of states $\\{s\\}$, and represents a set of real
attributes of instances $\\{i\\}$ when applying transformation $\\{t\\}$.

$\mathbb{R}$ is a set of relations $r$, and represents a set of relationships
$r$ between concept $c_{1}$ and concept $c_{2}$.

###  3.1 Architecture of Knowledge Map Model

Figure 2: Architecture of Knowledge Map

As illustrated in Figure 2, the architecture of OAK consists of the following
key components: (i) Knowledge Miner, (ii) Knowledge Wrapper and (iii)
Knowledge Management System.

  * •

Knowledge Miner is a key component, which is used to extract knowledge from
data; this component can be a Data Mining or an OLAP Analysis module.

    * –

Data Mining refers to mining tools and techniques, which are used in analyzing
datasets from various dimensions and perspectives, finding hidden knowledge
and summarizing the identified relationships. These techniques are
classification, clustering, regression, association rules.

    * –

OLAP Analysis refers to mining processes used in analyzing different
dimensions of multidimensional data, which is collected from multiple data
sources and stored in data warehouses.

  * •

Knowledge Wrapper is the main module to transform the knowledge from the
output of the Knowledge Miner module to the Knowledge Management System module
to store them. This module collects the mining result, identify the type of
the data mining task, data mining algorithms, list of agriculture concepts,
correlative transformation functions, and states. Then, it generates the KMap
representation before converting it into RDF turtles and import into the
Knowledge Management System.

  * •

Knowledge Management System is a graph database server, which supports RDF
triple storage and SPARQL protocol for the queries. This module receives the
domain knowledge from the pre-defined ontology, the mined knowledge
representations from the Knowledge Wrapper module, and then store in the RDF
Triple Storage as a set of RDF turtles.

In general, the proposed OAK model includes two knowledge layers. The first
layer is the background knowledge about agriculture. This layer is defined as
a core MKap and it is built from a pre-defined agricultural ontology (mainly
cropping knowledge in this project). This layer defines most of concepts
(agricultural entities related to crop) in the KMaps and common relations
between them. The second layer includes knowledge representations of data
mining results, which are mined from cropping datasets by data mining
algorithms (included in the Knowledge Miner module). These knowledge
representations are integrated into the Knowledge Management System by the
Knowledge Wrapper module.

###  3.2 Agriculture Ontology

In general, most ontologies describe classes (concepts), instances,
attributes, and relations. Moreover, some ontologies also include
restrictions, rules, axioms, and function terms. In our case, as a formal
presentation of KMaps, we propose an ontology with the following components:

  * •

Concepts: Concepts in the ontology include concepts in agriculture and
concepts for representing four main tasks of data mining. For example,
agriculture concepts have field, farmer, crop, organization, location,
product, while data mining concepts have clustering, classification,
regression, and association rule.

  * •

Transformations: They are pre-defined transformation functions of agriculture
concepts and existing data mining techniques for four main tasks of data
mining.

  * •

Relations: ways in which concepts (and then instances) can be related to
others. They are defined as the $\mathbb{R}$ set in definitions.

Figure 3: An overview of Agricultural Ontology architecture

At this stage, we propose an agricultural ontology AgriOnt for the purpose of
using it in the OAK model. The agricultural ontology contains 4 sub-domains:
agriculture, Internet-of-Thing (IoT), geographical, and the business sub-
domain (Figure 3). In addition, the ontology is also added concepts in data
mining domain as shown in Figure 4. These concepts and relations will be
knowledge frameworks to transform mined knowledge from data mining to
knowledge representations and import them into the knowledge maps.

Figure 4: Main data mining concepts in the ontology. Figure 5: A screenshot of Agricultural Ontology on Protege Table 1: AgriOnt’s ontology metrics Figure |  Core |  with Transformations |  with Geo-data
---|---|---|---
Axiom | 7,947 | 10,484 | 13,917
Logical axiom count | 3,782 | 5,194 | 7,892
Declaration axioms | 1,796 | 2,218 | 2,460
Class count | 361 | 361 | 361
Object property count | 90 | 90 | 90
Data property count | 156 | 156 | 156
Individual count | 1,183 | 1,605 | 1,847

After building a knowledge hierarchy, the ontology not only provides an
overview of the agriculture domain but also describes agricultural concepts,
and life cycles between seeds, plants, harvesting, transportation, and
consumption. It also gives the relationships between agricultural concepts and
related concepts, such as weather, soil conditions, fertilizers, farm
descriptions. In addition, this ontology also includes data mining concepts,
such as classification, clustering, regression, and association rule. These
concepts combined with agricultural concepts that are used to represent mined
knowledge. In fact, this ontology has 361 classes and over 7,947 axioms
related to agriculture (as shown in Table 1, and partly presented in [16]). As
result, the AgriOnt ontology can be used as the core ontology to build the
knowledge maps for agriculture. Moreover, this ontology with agricultural
hierarchy can help to integrate available resources to build larger and more
precise knowledge maps in agriculture domain.

###  3.3 Knowledge Management System

The knowledge consumption is handled in the Knowledge Wrapper module. This
wrapper transforms the mined knowledge to the Knowledge Maps layer. The
Knowledge Maps layer stores and indexes RDF-based data. The Knowledge Maps
layer provides the Data Access interfaces for query processing SPARQL engine.
The SPARQL engine enables the application developers to query data via a
SPARQL Endpoint or a SPARQL-based application in the Application layer
respectively. The SPARQL Endpoint serves one-shot queries using an extension
of SPARQL 1.1 query language.

In our approach, we use Apache Jena333https://jena.apache.org/index.html for
SPARQL Engine and Fuseki444https://jena.apache.org/documentation/fuseki2/ for
SPARQL Endpoint. Both Apache Jena and Fuseki are free and open source. Fuseki
is an HTTP interface to RDF data and it supports SPARQL for querying and
updating data.

###  3.4 Knowledge Wrapper

The procedure for mapping mined knowledge into a knowledge representation in
the ontology-based knowledge map is defined in the Knowledge Wrapper module.
The Knowledge Wrapper module is the main module to transform the mined
knowledge into a knowledge representation $k$ (as defined by
$k=(\\{i\\},\\{t\\},\\{s\\},\\{r\\})$ in Definition 1, Section 3) before
converting into RDF tubles and import them in to the RDF Triple storage. This
module has six steps (Figure 6):

  * •

Step 1, Identify model: Select data mining pattern based on the data mining
algorithm and generate the data mining instances (such as classification,
clustering, clustering, and association rule instances for the corresponding
data mining tasks) and link to the data mining algorithm as the transformation
objects of the data mining instances.

  * •

Step 2, Identify concepts: Identify agricultural concepts in mining results
and locate them in the ontology. Basically, these concepts occur in the mined
results as input features and predicting features, for example, SoilPH,
SeedRate, Nitrogen, Wheat, MeanYield.

  * •

Step 3, Generate instances: Generate agricultural instances of each located
concept and link them to data mining instances (in Step 1) based on the
framework of data mining tasks.

  * •

Step 4, Identify transformations: Identify transformations of each concept in
the mining results, locate them in the ontology part of the KMap, then link
them to the agricultural instances (in Step 3).

  * •

Step 5, Generate states: Identify states of each concept in the mining
results, generate states and link to instances (in Step 3) in the knowledge
representation.

  * •

Step 6, Generate turtles: Transform the knowledge representation into RDF
turtles and import them into the RDF triple storage.

In fact, the set of instances $\\{i\\}$ is created in Step 1 and Step 3, while
the set of transformations $\\{i\\}$ is created in Step 1 and Step 4. The set
of states $\\{s\\}$ is generated in Step 5, however, not all knowledge
representations have sets of states. For example, in the model to predict crop
yield, the input values only occur when the model is executed. Therefore, the
set of states for this knowledge representation is nearly none. Finally, set
of relations $\\{i\\}$ is based on relation isA, hasTransformation, hasState,
hasCondition, and predicts.

Figure 6: Generating knowledge representation the Ontology.

##  4 Experimental Results

Firstly, we have set up a SPARQL Server as a knowledge management system (cf.
Section 3.3) with Apache Jena and Fuseki library. The system has also created
a new knowledge map with a pre-defined ontology (as described in Section 3.2)
and several samples of knowledge representations, which are created manually
by Protege tool (as shown in Figure 5). The SPARQL Endpoint can be accessed at
http://localhost:3030/manage.html on local machine for query.

Basically, SPARQL queries can be run on the Endpoint with a web interface.
Figure 7 shows the results for the query ”What are conditions and the target
attribute of the knowledge model $Regressor\\_004$?”. The SPARQL query for
this question is shown bellow:

        PREFIX AgriOnt:  <http://www.ucd.ie/consus/AgriOnt#>
        PREFIX AgriKMap: <http://www.ucd.ie/consus/AgriKMap#>
        SELECT ?predicate1 ?object1 ?predicate2 ?object2
        WHERE {
            AgriKMap:Regressor_004 ?predicate1 ?object1 .
            ?object1  ?predicate2 ?object2 .
        }

Figure 7: Example of SPARQL query on AgriKMaps.

In this example, the mined knowledge for predicting soil pH [17] can be
represented as a knowledge representation $Regressor\\_004$ in the system.
Inputs of the model are pH information and the output of the model is also the
pH value (concept SoilPH), however, they used different transformations.
Specifically, input features are calculated as $pH_{min}$, $pH_{max}$, and
$pH_{avg}$ (three different transformations of SoilPH in the system) of
nearest neighbour fields, while the output feature is predicted as the
original pH value of the field (these conditions are defined as Soil_001,
Soil_002, Soil_003 and Soil_000 instance, as shown in Figure 7).

In addition, the knowledge management system based on the OAK model can be
benefit for both data scientists and agronomists. Data scientists can have
queries about potential transformations of agriculture attribute $c_{x}$ (for
example, Soil pH or Temperature), and these queries can be implemented by a
SPARQL query as below:

        PREFIX AgriOnt:  <http://www.ucd.ie/consus/AgriOnt#>
        PREFIX AgriKMap: <http://www.ucd.ie/consus/AgriKMap#>
        SELECT ?subject ?predicate ?object
        WHERE {
            ?subject AgriOnt:transformationOf AgriOnt:SoilPH .
            ?subject ?predicate ?object
        }

For agronomists and also farmers, they can have queries about potential
knowledge models or attributes to predict an attribute, such as crop yield.
The SPARQL query returns all potential knowledge models that are used to
predict CropYield as below:

        PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
        PREFIX AgriOnt:  <http://www.ucd.ie/consus/AgriOnt#>
        PREFIX AgriKMap: <http://www.ucd.ie/consus/AgriKMap#>
        SELECT ?subject ?predicate ?object
        WHERE {
            ?subject ?predicate ?object .
            ?subject AgriOnt:predicts ?object2 .
            ?object2  rdf:type AgriOnt:CropYield .
        }

Similarly, agronomists also can have queries for a specific state during
farming, such as how to get a high crop yield or how to identify the Leaf
brown spot disease. For example, the below query returns a knowledge
representation Classifier_016, which is study of Santanu Phadikar [20] for
detecting 4 rices diseases, including Leaf brown spot, Rice blast, Sheath rot,
and Bacterial blight. In which, Sheath rot is one of four predicting states of
the model. The query also provides all information related to input
attributes, prediction method and evaluation information (Figure 8).

        PREFIX rdf: <http://www.w3.org/1999/02/22-rdf-syntax-ns#>
        PREFIX AgriOnt:  <http://www.ucd.ie/consus/AgriOnt#>
        PREFIX AgriKMap: <http://www.ucd.ie/consus/AgriKMap#>
        SELECT ?subject1 ?predicate2 ?object2
        WHERE {
            ?subject1  ?predicate1 ?object1 .
            ?object1   AgriOnt:hasState   AgriOnt:SheathRot .
       ΨΨ?subject1  ?predicate2 ?object2 .
        }
        LIMIT 100

Figure 8: Returns of SPARQL query for Sheath rot disease

##  5 Conclusion

In this paper, we present an architecture for the OAK - an ontology-based
knowledge map model to represent mined knowledge from data mining tasks in
digital agriculture. The architecture includes Knowledge Miner, Knowledge
Wrapper, Knowledge Management modules based on an pre-defined ontology. We
have also built an agricultural ontology to provide the domain knowledge in
agriculture and a knowledge management system to store knowledge
representations and support the knowledge retrieval efficiently.

With the proposed ontology-based knowledge map model, the knowledge management
system based on this model is a promised architecture for handling mined
knowledge in agriculture as well as other domains. As result, we plan to
import more knowledge items in the digital agriculture domain into the
knowledge management system for retrieval. Moreover, the knowledge management
system also supports a knowledge browser function as a further method to
access knowledge for both data scientists and agronomists.

#### Acknowledgment

This work is part of CONSUS and is supported by the the SFI Strategic
Partnerships Programme (16/SPP/3296) and is co-funded by Origin Enterprises
Plc.

## References

  * [1] Aggelopoulou, A.D., Bochtis, D., Fountas, S., Swain, K.C., Gemtos, T.A., Nanos, G.D.: Yield prediction in apple orchards based on image processing. Precis. Agric. 12(3), 448–456 (2011)
  * [2] Bargent, J.: 11 Steps to Building a Knowledge Map (2002). www.providersedge. com/docs/km articles/11 Steps to Building a K Map.pdf
  * [3] Bishop, T.F.A., McBratney, A.B.: A comparison of prediction methods for the creation of field-extent soil property maps. Geoderma 103(1–2), 149–160 (2001)
  * [4] Chen, Y., Kuang, J., Cheng, D., Zheng, J., Gao, M., Zhou, A.: AgriKG: an agricultural knowledge graph and its applications. In: Li, G., Yang, J., Gama, J., Natwichai, J., Tong, Y. (eds.) DASFAA 2019. LNCS, vol. 11448, pp. 533–537. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-18590-9 81
  * [5] Chenglin, Q., Qing, S., Pengzhou, Z., Hui, Y.: Cn-MAKG: China meteorology and agriculture knowledge graph construction based on semi-structured data. In: 2018 IEEE/ACIS 17th International Conference on Computer and Information Science (ICIS), pp. 692–696. IEEE (2018)
  * [6] Eppler, M.J.: A comparison between concept maps, mind maps, conceptual diagrams, and visual metaphors as complementary tools for knowledge construction and sharing. Inf. Vis. 5(3), 202–210 (2006)
  * [7] Karimi, Y., Prasher, S.O., Patel, R.M., Kim, S.H.: Application of support vector machine technology for weed and nitrogen stress detection in corn. Comput. Electron. Agric. 51(1–2), 99–109 (2006)
  * [8] Kim, S., Suh, E., Hwang, H.: Building the knowledge map: an industrial case study. J. Knowl. Manag. 7(2), 34–45 (2003)
  * [9] Le-Khac, N.-A., Aouad, L.M., Kechadi, M.-T.: Knowledge map: toward a new approach supporting the knowledge management in distributed data mining. In: Third International Conference on Autonomic and Autonomous Systems (ICAS 2007), p. 67. IEEE (2007)
  * [10] Le-Khac, N.-A., Kechadi, M.T.: Admire framework: distributed data mining on data-grid platforms. In: International Conference on Software and Data Technologies (ICSOFT 2006), Setubal, Portugal (2006)
  * [11] Lecocq, R., Valcartier, D.: Knowledge mapping: a conceptual model. Quebec: Defense Research and Development Canada-Valcartier. Acedido Dezembro, vol. 21, p. 2011 (2006)
  * [12] Liu, J., Goering, C.E., Tian, L.: A neural network for setting target corn yields. Trans. ASAE 44(3), 705 (2001)
  * [13] Liu, L., Li, J., Lv, C.: A method for enterprise knowledge map construction based on social classification. Syst. Res. Behav. Sci. Off. J. Int. Fed. Syst. Res. 26(2), 143–153 (2009)
  * [14] Maltas, A., Charles, R., Jeangros, B., Sinaj, S.: Effect of organic fertilizers and reduced-tillage on soil properties, crop nitrogen response and crop yield: results of a 12-year experiment in Changins, Switzerland. Soil Tillage Res. 126, 11–18 (2013)
  * [15] Mansingh, G., Osei-Bryson, K.-M., Reichgelt, H.: Building ontology-based knowledge maps to assist knowledge process outsourcing decisions. Knowl. Manag. Res. Pract. 7(1), 37–51 (2009)
  * [16] Ngo, Q.H., Le-Khac, N.-A., Kechadi, T.: Ontology based approach for precision agriculture. In: Kaenampornpan, M., Malaka, R., Nguyen, D.D., Schwind, N. (eds.) MIWAI 2018. LNCS (LNAI), vol. 11248, pp. 175–186. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03014-8 15
  * [17] Ngo, Q.H., Le-Khac, N.-A., Kechadi, T.: Predicting soil pH by using nearest fields. In: Bramer, M., Petridis, M. (eds.) SGAI 2019. LNCS (LNAI), vol. 11927, pp. 480–486. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34885-4 40
  * [18] Pantazi, X.E., Moshou, D., Alexandridis, T., Whetton, R.L., Mouazen, A.M.: Wheat yield prediction using machine learning and advanced sensing techniques. Comput. Electron. Agric. 121, 57–65 (2016)
  * [19] Pei, X., Wang, C.: A study on the construction of knowledge map in matrix organizations. In: 2009 International Conference on Management and Service Science (2009)
  * [20] Das, A.K., Phadikar, S., Sil, J.: Rice diseases classification using feature selection and rule generation techniques. Comput. Electron. Agric. 90, 76–85 (2013)
  * [21] Shangguan, W., et al.: A China data set of soil properties for land surface modeling. J. Adv. Model. Earth Syst. 5(2), 212–224 (2013)
  * [22] Vail, E.F.: Knowledge mapping: getting started with knowledge management. Inf. Syst. Manag. 16, 10–23 (1999)
  * [23] Wang, F., Yang, S., Yang, W., Yang, X., Jianli, D.: Comparison of machine learning algorithms for soil salinity predictions in three dryland oases located in Xinjiang Uyghur Autonomous Region (XJUAR) of China. Eur. J. Remote. Sens. 52(1), 256–276 (2019)