Sense Disambiguation: From Natural Language Words to Mathematical Terms

International Joint Conference on Natural Language Processing, pages 809–814, Nagoya, Japan, 14-18 October 2013. Sense disambiguation: from natural language words to mathematical terms Minh-Quoc Nghiem, 1 Giovanni Yoko Kristianto, 2 Goran Topi´c, 3 Akiko Aizawa 2,3 1 The Graduate University for Advanced Studies, Tokyo, Japan 2 The University of Tokyo, Tokyo, Japan 3 National Institute of Informatics, Tokyo, Japan {nqminh, giovanni, goran topic, aizawa}@nii.ac.jp Abstract This paper addresses the open prob- lem of mathematical term sense disam- biguation. We introduce a method that uses a MathML parallel markup corpus to generate relevant training and testing datasets. Based on the dataset generated, we use Support Vector Machine classifier to disambiguate the sense of mathematical terms. Experimental results indicate we can generate such data automatically and with reasonable accuracy. 1 Introduction Word-sense disambiguation (WSD) refers to the process of identifying the correct sense or mean- ing of a word in a sentence when the word has multiple meanings. WSD remains a difficult open problem in natural language processing. Current WSD systems are based on supervised, unsuper- vised, and knowledge-based approaches (Navigli, 2009). This paper focuses on the problem of dis- ambiguating the sense of mathematical terms oc- curring within normal text, an aspect little dis- cussed to date. The problem of achieving automated under- standing of mathematical expressions can be il- lustrated quite clearly. For instance, depend- ing on context, the mathematical term δ can be interpreted to refer to Kronecker Delta, Dirac Delta, Discrete Delta, or simply to a variable δ. Another example is i, which can be interpreted to mean the imaginary constant, the index variable, or the bound variable of an operation. Other ex- amples include α, β, σ, φ, ω, Φ, B, H, x, y, sim. In many such cases, disambiguation can play a crucial role in the automated understand- ing, translation, and calculation of mathematical expressions. One major issue in early research on machine understanding of mathematical terms found in text was the lack of evaluation datasets. A previ- ous study (Wolska et al., 2011) was based on a small evaluation set of 200 mathematical expres- sions annotated by experts. Clearly, large sam- ples of sense-tagged data would require signif- icant human annotation and labor. Fortunately, then, Ide et al. (2002) showed that sense distinc- tions derived from cross-lingual information are at least as reliable as those made by human annota- tors. The novel research described in our paper presents a fully automated method for generating large samples of mathematical terms with sense- tagged data. As part of the effort described here to address mathematical term sense disambiguation (MTSD), we first propose a method that uses a MathML par- allel markup corpus to generate training and test- ing datasets. Second, we propose heuristics that improve alignment results for the parallel markup corpus. Third, we present a classification-based approach to the MTSD problem. To the best of our knowledge, this study is the first to make use of parallel corpora to address MTSD. The rest of this paper …

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