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Math-word embedding in math search and semantic extraction

Author

Listed:
  • André Greiner-Petter

    (University of Wuppertal)

  • Abdou Youssef

    (The George Washington University
    NIST)

  • Terry Ruas

    (University of Wuppertal)

  • Bruce R. Miller

    (NIST)

  • Moritz Schubotz

    (University of Wuppertal
    FIZ Karlsruhe)

  • Akiko Aizawa

    (National Institute of Informatics)

  • Bela Gipp

    (University of Wuppertal)

Abstract

Word embedding, which represents individual words with semantically fixed-length vectors, has made it possible to successfully apply deep learning to natural language processing tasks such as semantic role-modeling, question answering, and machine translation. As math text consists of natural text, as well as math expressions that similarly exhibit linear correlation and contextual characteristics, word embedding techniques can also be applied to math documents. However, while mathematics is a precise and accurate science, it is usually expressed through imprecise and less accurate descriptions, contributing to the relative dearth of machine learning applications for information retrieval in this domain. Generally, mathematical documents communicate their knowledge with an ambiguous, context-dependent, and non-formal language. Given recent advances in word embedding, it is worthwhile to explore their use and effectiveness in math information retrieval tasks, such as math language processing and semantic knowledge extraction. In this paper, we explore math embedding by testing it on several different scenarios, namely, (1) math-term similarity, (2) analogy, (3) numerical concept-modeling based on the centroid of the keywords that characterize a concept, (4) math search using query expansions, and (5) semantic extraction, i.e., extracting descriptive phrases for math expressions. Due to the lack of benchmarks, our investigations were performed using the arXiv collection of STEM documents and carefully selected illustrations on the Digital Library of Mathematical Functions (DLMF: NIST digital library of mathematical functions. Release 1.0.20 of 2018-09-1, 2018). Our results show that math embedding holds much promise for similarity, analogy, and search tasks. However, we also observed the need for more robust math embedding approaches. Moreover, we explore and discuss fundamental issues that we believe thwart the progress in mathematical information retrieval in the direction of machine learning.

Suggested Citation

  • André Greiner-Petter & Abdou Youssef & Terry Ruas & Bruce R. Miller & Moritz Schubotz & Akiko Aizawa & Bela Gipp, 2020. "Math-word embedding in math search and semantic extraction," Scientometrics, Springer;Akadémiai Kiadó, vol. 125(3), pages 3017-3046, December.
    • Handle: RePEc:spr:scient:v:125:y:2020:i:3:d:10.1007_s11192-020-03502-9
    DOI: 10.1007/s11192-020-03502-9
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    References listed on IDEAS

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    1. Rudolph, Maja & Ruiz, Francisco & Athey, Susan & Blei, David, 2017. "Structured Embedding Models for Grouped Data," Research Papers repec:ecl:stabus:3597, Stanford University, Graduate School of Business.
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    Cited by:

    1. Chen, Hongshu & Jin, Qianqian & Wang, Ximeng & Xiong, Fei, 2022. "Profiling academic-industrial collaborations in bibliometric-enhanced topic networks: A case study on digitalization research," Technological Forecasting and Social Change, Elsevier, vol. 175(C).
    2. Qianqian Jin & Hongshu Chen & Ximeng Wang & Tingting Ma & Fei Xiong, 2022. "Exploring funding patterns with word embedding-enhanced organization–topic networks: a case study on big data," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(9), pages 5415-5440, September.

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