Improving the Representation and Conversion of Mathematical Formulae by Considering their Textual Context

Abstract

Mathematical formulae represent complex semantic information in a concise form. Especially in Science, Technology, Engineering, and Mathematics, mathematical formulae are crucial to communicate 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.

Fast Linking of Mathematical Wikidata Entities in Wikipedia Articles Using Annotation Recommendation

“…The challenge of Formula Concept retrieval [18] (a method for MathEL) can roughly be split into the discovery (defining concepts by exploring some instances) of Formula Concepts and their recognition (matching new instances to prior defined concepts represented by name 6 ). A Wikidata Entity Linking markup to for L A T E X and MathML was introduced and discussed in [20] and [14]. The proposed markup should be used by authors of documents in the STEM disciplines to semantically annotate mathematical content in documents.…”

“…There have been efforts to automatically retrieve the semantics of identifiers from the surrounding text [23]. A benchmark MathMLben [20] was created containing formulae from Wikipedia, the arXiV and the DLMF, which were augmented by Wikidata markup [14]. Greiner-Petter and Schubotz [5] examine distributions of mathematical notation on two large corporae from the arXiv 4 and zbMATH 5 repository.…”

“…A balanced combination of mathematical and textual elements is required for the linking performance to be reliable. Besides linking to Wikipedia, Schubotz, Scharpf et al [20,14] describe linking mathematical formula content to Wikidata, both in MathML and L A T E Xmarkup. To extend classical citations by mathematical, they call for a 'Formula Concept Discovery (FCD) and Formula Concept Recognition (FCR) challenge' to elaborate automated MathEL.…”

Mathematical Information Retrieval

“…NLP techniques often play a critical role in bridging the gap between presentation and semantic representations of math formulae. Recent studies on this topic include variable typing (Stathopoulos et al 2018), using the textual context for transformation from a presentation level to semantic level (Schubotz et al 2018), and identifying declarations of mathematical objects (Lin et al 2019).…”

Data-Driven Recognition and Extraction of PDF Document Elements

“…Due to the challenges raised by PDF documents, many approaches use the original source data, just as the original Microsoft Word document or Latex code and resources in order to implement their use cases. For instance, Scharpf et al [12][13][14] focus their research on discovering and recognizing mathematical formulas in scientific publications in order disambiguate formula identifiers so that mathematical publications become interpretable by computers. Groza et al [15,16], on the other hand, deal with the insertion of metadata at the phase of writing in order to improve the retrievability of scientific publications.…”