Improving the representation and conversion of mathematical formulae by considering their textual context

Published

May 1, 2018

Author(s)

Howard S. Cohl, Moritz Schubotz, Andre Greiner Petter, Philipp Scharpf, Norman Meuschke, Bela Gipp

Abstract

Mathematical formulae represent complex semantic information in a concise form. Especially in Science, Technology, Engineering, and Mathematics, mathematical formulae are crucial for communicating information, e.g., in scientific papers, and to perform computations using computer algebra systems. Enabling computers to access the information encoded in mathematical formulae requires machine-readable formats that can represent both the presentation and content, i.e., the semantics, of formulae. Exchanging such information between systems additionally requires conversion methods for mathematical representation formats. We analyze how the semantic enrichment of formulae improves the format conversion process and show that considering the textual context of formulae reduces the error rate of such conversions. Our main contributions are: (1) providing an openly available benchmark dataset for the mathematical format conversion task consisting of a newly created test collection, an extensive, manually curated gold standard and task-specific evaluation metrics; (2) performing a quantitative evaluation of state-of-the-art tools for mathematical format conversions; (3) presenting a new approach that considers the textual context of formulae to reduce the error rate for mathematical format conversions. Our benchmark dataset facilitates future research on mathematical format conversions as well as research on many problems in mathematical information retrieval. Because we annotated and linked all components of formulae, e.g., identifiers, operators and other entities, to Wikidata entries, the gold standard can, for instance, be used to train methods for formula concept discovery and recognition. Such methods can then be applied to improve mathematical information retrieval systems, e.g., for semantic formula search, recommendation of mathematical content, or detection of mathematical plagiarism.

Citation

TUGBOAT - The Communications of the TeX Users Group

Volume

39

Issue

3

Pub Type

Journals

Download Paper

https://doi.org/10.1145/3197026.3197058

Local Download

Citation

Cohl, H. , Schubotz, M. , Greiner, A. , Scharpf, P. , Meuschke, N. and Gipp, B. (2018), Improving the representation and conversion of mathematical formulae by considering their textual context, TUGBOAT - The Communications of the TeX Users Group, [online], https://doi.org/10.1145/3197026.3197058 (Accessed April 26, 2024)