Evaluating and Improving the Extraction of Mathematical Identifier Definitions

Mathematical formulae in academic texts significantly contribute to the overall semantic content of such texts, especially in the fields of Science, Technology, Engineering and Mathematics. Knowing the definitions of the identifiers in mathematical formulae is essential to understand the semantics of the formulae. Similar to the sense-making process of human readers, mathematical information retrieval systems can analyze the text that surrounds formulae to extract the definitions of identifiers occurring in the formulae. Several approaches for extracting the definitions of mathematical identifiers from documents have been proposed in recent years. So far, these approaches have been evaluated using different collections and gold standard datasets, which prevented comparative performance assessments. To facilitate future research on the task of identifier definition extraction, we make three contributions. First, we provide an automated evaluation framework, which uses the dataset and gold standard of the NTCIR-11 Math Retrieval Wikipedia task. Second, we compare existing identifier extraction approaches using the developed evaluation framework. Third, we present a new identifier extraction approach that uses machine learning to combine the well-performing features of previous approaches. The new approach increases the precision of extracting identifier definitions from 17.85% to 48.60%, and increases the recall from 22.58% to 28.06%. The evaluation framework, the dataset and our source code are openly available at: https://ident.formulasearchengine.com.