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Discovering Mathematical Objects of Interest : A Study of Mathematical Notations

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2020

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HUANG, Yennun, ed. and others. WWW '20: Proceedings of The Web Conference 2020. New York, NY: Association for Computing Machinery, 2020, pp. 1445-1456. ISBN 978-1-4503-7023-3. Available under: doi: 10.1145/3366423.3380218

Zusammenfassung

Mathematical notation, i.e., the writing system used to communicate concepts in mathematics, encodes valuable information for a variety of information search and retrieval systems. Yet, mathematical notations remain mostly unutilized by today’s systems. In this paper, we present the first in-depth study on the distributions of mathematical notation in two large scientific corpora: the open access arXiv (2.5B mathematical objects) and the mathematical reviewing service for pure and applied mathematics zbMATH (61M mathematical objects). Our study lays a foundation for future research projects on mathematical information retrieval for large scientific corpora. Further, we demonstrate the relevance of our results to a variety of use-cases. For example, to assist semantic extraction systems, to improve scientific search engines, and to facilitate specialized math recommendation systems.

The contributions of our presented research are as follows: (1) we present the first distributional analysis of mathematical formulae on arXiv and zbMATH; (2) we retrieve relevant mathematical objects for given textual search queries (e.g., linking with ‘Jacobi polynomial’); (3) we extend zbMATH’s search engine by providing relevant mathematical formulae; and (4) we exemplify the applicability of the results by presenting auto-completion for math inputs as the first contribution to math recommendation systems. To expedite future research projects, we have made available our source code and data.

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The Web Conference 2020, 20. Apr. 2020 - 24. Apr. 2020, Taipei, Taiwan
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ISO 690GREINER-PETTER, André, Moritz SCHUBOTZ, Fabian MÜLLER, Corinna BREITINGER, Howard COHL, Akiko AIZAWA, Bela GIPP, 2020. Discovering Mathematical Objects of Interest : A Study of Mathematical Notations. The Web Conference 2020. Taipei, Taiwan, 20. Apr. 2020 - 24. Apr. 2020. In: HUANG, Yennun, ed. and others. WWW '20: Proceedings of The Web Conference 2020. New York, NY: Association for Computing Machinery, 2020, pp. 1445-1456. ISBN 978-1-4503-7023-3. Available under: doi: 10.1145/3366423.3380218
BibTex
@inproceedings{GreinerPetter2020Disco-53714,
  year={2020},
  doi={10.1145/3366423.3380218},
  title={Discovering Mathematical Objects of Interest : A Study of Mathematical Notations},
  isbn={978-1-4503-7023-3},
  publisher={Association for Computing Machinery},
  address={New York, NY},
  booktitle={WWW '20: Proceedings of The Web Conference 2020},
  pages={1445--1456},
  editor={Huang, Yennun},
  author={Greiner-Petter, André and Schubotz, Moritz and Müller, Fabian and Breitinger, Corinna and Cohl, Howard and Aizawa, Akiko and Gipp, Bela}
}
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    <dcterms:abstract xml:lang="eng">Mathematical notation, i.e., the writing system used to communicate concepts in mathematics, encodes valuable information for a variety of information search and retrieval systems. Yet, mathematical notations remain mostly unutilized by today’s systems. In this paper, we present the first in-depth study on the distributions of mathematical notation in two large scientific corpora: the open access arXiv (2.5B mathematical objects) and the mathematical reviewing service for pure and applied mathematics zbMATH (61M mathematical objects). Our study lays a foundation for future research projects on mathematical information retrieval for large scientific corpora. Further, we demonstrate the relevance of our results to a variety of use-cases. For example, to assist semantic extraction systems, to improve scientific search engines, and to facilitate specialized math recommendation systems.&lt;br /&gt;&lt;br /&gt;The contributions of our presented research are as follows: (1) we present the first distributional analysis of mathematical formulae on arXiv and zbMATH; (2) we retrieve relevant mathematical objects for given textual search queries (e.g., linking with ‘Jacobi polynomial’); (3) we extend zbMATH’s search engine by providing relevant mathematical formulae; and (4) we exemplify the applicability of the results by presenting auto-completion for math inputs as the first contribution to math recommendation systems. To expedite future research projects, we have made available our source code and data.</dcterms:abstract>
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