Geodesic
A system for automatic construction of knowledge graphs of mathematical documents
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 165 (2023) no. 3, pp. 264-281 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

This article outlines the process of creating an automated system for knowledge graph construction from collections of mathematical documents in LATEX format. The MathCollectionOntology, which defines the types of objects and relationships in knowledge graphs, was developed. The introduced toolkit includes methods for extracting mathematical terms, browsing and identifying document topics, extracting entities from LATEX code, and calculating statistical parameters of the graph. The parsed entities are mathematical terms, topics generated through the Latent Dirichlet Allocation, UDC codes, used formulas, author affiliations, cited literature, and others. The knowledge graph captures each extracted object using specific types of relationships defined in the MathCollectionOntology. Here, a knowledge graph was coined for a collection of articles published in Izvestiya VUZov. Matematika journal (1114 Russian-language documents in LATEX format). The thematic terms of the document topics were described. The quantitative parameters of the constructed knowledge graph were obtained.
Keywords: knowledge graph construction, linked open data, topic modeling, mathematical article, text processing. 
@article{UZKU_2023_165_3_a6,
     author = {O. A. Nevzorova and B. T. Gizatullin},
     title = {A system for automatic construction of knowledge graphs of mathematical documents},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {264--281},
     year = {2023},
     volume = {165},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2023_165_3_a6/}
}
TY  - JOUR
AU  - O. A. Nevzorova
AU  - B. T. Gizatullin
TI  - A system for automatic construction of knowledge graphs of mathematical documents
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2023
SP  - 264
EP  - 281
VL  - 165
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/UZKU_2023_165_3_a6/
LA  - ru
ID  - UZKU_2023_165_3_a6
ER  - 
%0 Journal Article
%A O. A. Nevzorova
%A B. T. Gizatullin
%T A system for automatic construction of knowledge graphs of mathematical documents
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2023
%P 264-281
%V 165
%N 3
%U http://geodesic.mathdoc.fr/item/UZKU_2023_165_3_a6/
%G ru
%F UZKU_2023_165_3_a6
O. A. Nevzorova; B. T. Gizatullin. A system for automatic construction of knowledge graphs of mathematical documents. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 165 (2023) no. 3, pp. 264-281. http://geodesic.mathdoc.fr/item/UZKU_2023_165_3_a6/

[1] National Research Council. Developing a 21st Century Global Library for Mathematics Research, Natl. Acad. Press, Washington, DC, 2014, 142 pp. | DOI

[2] P. D.F. Ion, S. M. Watt, “The Global Digital Mathematics Library and the International Mathematical Knowledge Trust”, CICM 2017: Intelligent Computer Mathematics, Lecture Notes in Computer Science, 10383, eds. H. Geuvers, M. England, O. Hasan, F. Rabe, O. Teschke, Springer, Cham, 2017, 56–69 | DOI | Zbl

[3] T. Bouche, J. Rákosnik, “Report on the EuDML External Cooperation Model”, Proc. Joint Math. Meet. AMS Special Session (San Diego, 2013), 99–108 https://www.emis.de/proceedings/TIEP2013/07bouche_rakosnik.pdf

[4] J. Carette, W. M. Farmer, M. Kohlhase, F. Rabe, “Big math and the one-brain barrier: The tetrapod model of mathematical knowledge”, Math. Intell, 43 (2021), 78–87 | DOI | MR | Zbl

[5] J. Borwein, E.M. Rocha, J.F. Rodrigues (eds), Communicating Mathematics in the Digital Era, 1st ed., A K Peters, CRC Press, Wellesley, MA, 2008, 325 pp. | DOI | MR | Zbl

[6] T. Bouche, “Digital mathematics libraries: The good, the bad, the ugly”, Math. Comput. Sci, 3 (2010), 227–241 | DOI | Zbl

[7] A. M. Elizarov, E. K. Lipachev, D. S. Zuev, “Digital mathematical libraries: Overview of implementations and content management services”, CEUR Workshop Proc., 2022, 2017, 317–325 https://ceur-ws.org/Vol-2022/paper49.pdf

[8] A. Hogan, C. Gutierrez, M. Cochez, G. de Melo, S. Kirrane, A. Polleres, R. Navigli, A. C. N. Ngomo, S. M. Rashid, L. Schmelzeisen, S. Staab, E. Blomqvist, C. d'Amato, J. E. Labra Gayo, S. Neumaier, A. Rula, J. Sequeda, A. Zimmermann, Knowledge Graphs, Synthesis Lectures on Data, Semantics, and Knowledge, Springer, Cham, 2022, xix+237 pp. | DOI

[9] J. Lehmann, R. Isele, M. Jakob, A. Jentzsch, D. Kontokostas, P. N. Mendes, S. Hellmann, M. Morsey, P. V. Kleef, S. Auer, C. Bizer, “DBpedia A large-scale, multilingual knowledge base extracted from Wikipedia”, Semantic Web, 6:2 (2015), 167–195 | DOI

[10] K. Bollacker, R. Cook, P. Tufts, “Freebase: A shared database of structured general human knowledge”, Proc. 22nd Natl. Conf. on Artificial Intelligence, v. 2, AAAI Press, Vancouver, 2007, 1962–1963

[11] D. Vrandečić, M. Krötzsch, “Wikidata: A free collaborative knowledge base”, Commun. ACM, 57:10 (2014), 78–85 | DOI

[12] J. Hoffart, F. M. Suchanek, K. Berberich, E. Lewis-Kelham, G. de Melo, G. Weikum, “YAGO2: Exploring and querying world knowledge in time, space, context, and many languages”, Proc. 20th Int. World Wide Web Conf. (Hyderabad, 2011), 2011, 229–232 | DOI

[13] A. Carlson, J. Betteridge, R. C. Wang, E. R. Hruschka, T. M. Mitchell, “Coupled semi supervised learning for information extraction”, Proc. 3rd ACM Int. Conf. on Web Search and Data Mining, Assoc. Comput. Mach., New York, NY, 2010, 101–110 | DOI

[14] N. Noy, Y. Gao, A. Jain, A. Narayanan, A. Patterson, J. Taylor, “Industry-scale knowledge graphs: Lessons and challenges”, Commun. ACM, 62:8 (2019), 36–43 | DOI

[15] S. Peroni, D. M. Shotton, F. Vitali, “One year of the OpenCitations Corpus: Releasing RDF based scholarly citation data into the public domain”, ISWC 2017: The Semantic Web ISWC 2017, Lecture Notes in Computer Science, 10588, eds. C. d'Amato, M. Fernandez, V. Tamma, F. Lecue, P. Cudré-Mauroux, J. Sequeda, C. Lange, J. Heflin, Springer, Cham, 2017, 184–192 | DOI

[16] A. Iana, S. Jung, P. Naeser, A. Birukou, S. Hertling, H. Paulheim, “Building a conference recommender system based on SciGraph and WikiCFP”, SEMANTiCS 2019: Semantic Systems. The Power of AI and Knowledge Graphs, Lecture Notes in Computer Science, 11702, eds. M. Acosta, P. Cudré-Mauroux, M. Maleshkova, T. Pellegrini, H. Sack, Y. Sure-Vetter, Springer, Cham, 2019, 117–123 | DOI

[17] M. Frärber, “The Microsoft Academic Knowledge Graph: A linked data source with 8 billion triples of scholarly data”, ISWC 2019: The Semantic Web ISWC 2019, Lecture Notes in Computer Science, 11779, eds. C. Ghidini, O. Hartig, M. Maleshkova, V. Svátek, I. Cruz, A. Hogan, J. Song, M. Lefrancois, F. Gandon, Springer, Cham, 2019, 113–129 | DOI

[18] O. Nevzorova, N. Zhiltsov, D. Zaikin, O. Zhibrik, A. Kirillovich, V. Nevzorov, E. Birialtsev, “Bringing math to LOD: A semantic publishing platform prototype for scientific collections in mathematics”, ISWC 2013: The Semantic Web ISWC 2013, Lecture Notes in Computer Science, 8218, eds. H. Alani, L. Kagal, A. Fokoue, P. Groth, C. Biemann, J.X. Parreira, L. Aroyo, N. Noy, C. Welty, K. Janowicz, Springer, Berlin–Heidelberg, 2013, 379–394 | DOI

[19] G. Buchgeher, D. Gabauer, J. Martinez-Gil, L. Ehrlinger, “Knowledge graphs in manufacturing and production: A systematic literature review”, IEEE Access., 9 (2021), 55537–55554 | DOI

[20] Z. Zhao, S. K. Han, I. M. So, “Architecture of knowledge graph construction techniques”, Int. J. Pure Appl. Math, 118:19 (2018), 1869–1883

[21] M. Kaufmann, G. Wilke, E. Portmann, K. Hinkelmann, “Combining bottom-up and top down generation of interactive knowledge maps for enterprise search”, KSEM 2014: Knowledge Science, Engineering and Management, Lecture Notes in Computer Science, 8793, eds. R. Buchmann, C.V. Kifor, J. Yu, Springer, Cham, 2014, 186–197 | DOI

[22] D. Fensel, U. Simsek, K. Angele, E. Huaman, E. Kärle, O. Panasiuk, I. Toma, J. Umbrich, A. Wahler, Knowledge Graphs. Methodology, Tools and Selected Use Cases, Springer, Cham, 2020, xvi+148 pp. | DOI

[23] P. Schneider, T. Schopf, J. Vladika, M. Galkin, E. Simperl, F. Matthes, A Decade of Knowledge Graphs in Natural Language Processing: A Survey, 2022, arXiv: 2210.00105 | DOI

[24] P. Schneider, T. Schopf, J. Vladika, M. Galkin, E. Simperl, F. Matthes, “A decade of knowledge graphs in natural language processing: A survey”, Assoc. Comput. Linguist., Proc. 2nd Conf. of the Asia-Pacific Chapter of the Association for Computational Linguistics and 12th Int. Joint Conf. on Natural Language Processing, v. 1, eds. Y. He, H. Ji, S. Li, Y. Liu, C.-H. Chang, 2022, 601–614

[25] S. Pan, L. Luo, Y. Wang, C. Chen, J. Wang, X. Wu, Unifying Large Language Models and Knowledge Graphs: A Roadmap, 2023, arXiv: 2306.08302 | DOI

[26] T. Shen, F. Zhang, J. Cheng, “A comprehensive overview of knowledge graph completion”, Knowl. Based Syst., 255 (2022), 109597 | DOI

[27] Y. Zhu, X. Wang, J. Chen, S. Qiao, Y. Ou, Y. Yao, S. Deng, H. Chen, N. Zhang, LLMs for Knowledge Graph Construction and Reasoning: Recent Capabilities and Future Opportunities, 2023, arXiv: 2305.13168 | DOI

[28] A. M. Elizarov, A. V. Kirillovich, E. K. Lipachev, O. A. Nevzorova, “OntoMathPRO : An ontology of mathematical knowledge”, Dokl. Math., 106:3 (2022), 429–435 | DOI | MR | Zbl

[29] A. V. Kirillovich, O. A. Nevzorova, E. K. Lipachev, “OntoMathPRO 2.0 ontology: Updates of formal model”, Lobachevskii J. Math.., 43:12 (2022), 3504–3514 | DOI

[30] O. A. Nevzorova, M. V. Falileeva, A. V. Kirillovich, E. K. Lipachev, L. R. Shakirova, A. E. Dyupina, “OntoMathEdu educational ontology: Problems of ontological engineering”, Pattern Recognit. Image Anal, 33:3 (2023), 460–466 | DOI

[31] O. M. Ataeva, V. A. Serebryakov, N. P. Tuchkova, “Ontological approach to a knowledge graph construction in a semantic library”, Lobachevskii J. Math, 44:6 (2023), 2229–2239 | DOI | MR

[32] J. Wang, Math-KG: Construction and Applications of Mathematical Knowledge Graph, 2022, arXiv: 2205.03772 | DOI

[33] M. Röder, A. Both, A. Hinneburg, “Exploring the space of topic coherence measures”, Proc. 8th ACM Int. Conf. on Web Search and Data Mining, WSDM'15, Assoc. Comput. Mach., New York, NY, 2015, 399–408 | DOI

[34] D. M. Blei, A. Y. Ng, M. I. Jordan, “Latent Dirichlet allocation”, J. Mach. Learn. Res, 3 (2003), 993–1022 | Zbl

[35] I. Porteous, D. Newman, A. Ihler, A. Asuncion, P. Smyth, M. Welling, “Fast collapsed Gibbs sampling for latent Dirichlet allocation”, Proc. 14th ACM SIGKDD Int. Conf. on Knowledge Discovery and Data Mining, KDD'08, Assoc. Comput. Mach., New York, NY, 2008, 569–577 | DOI