Mathematical Information Retrieval based on Type Embeddings and Query Expansion

Proceedings of COLING 2016, the 26th International Conference on Computational Linguistics: Technical Papers, pages 2344–2355, Osaka, Japan, December 11-17 2016. Mathematical Information Retrieval based on Type Embeddings and Query Expansion Yiannos A. Stathopoulos Simone Teufel Computer Laboratory, University of Cambridge 15 JJ Thomson Avenue, Cambridge, UK {yiannos.stathopoulos,simone.teufel}@cl.cam.ac.uk Abstract We present an approach to mathematical information retrieval (MIR) that exploits a special kind of technical terminology, referred to as a mathematical type. In this paper, we present and eval- uate a type detection mechanism and show its positive effect on the retrieval of research-level mathematics. Our best model, which performs query expansion with a type-aware embedding space, strongly outperforms standard IR models with state-of-the-art query expansion (vector space-based and language modelling-based), on a relatively new corpus of research-level queries. 1 Introduction Mathematical information retrieval (MIR) systems, such as MathWebSearch (Kohlhase and Prodescu, 2013; Hambasan et al., 2014), MIaS (Sojka and L´ıˇska, 2011) and Tangent (Pattaniyil and Zanibbi, 2014) have demonstrated that indexing and matching of formulae is beneficial to MIR. However, despite the sophistication of these methods, they leave elements of the natural language of mathematics largely unexploited. In contrast to general text, text in mathematics follows strong domain-specific conventions governing how content is presented (Ganesalingam, 2008). This is particularly so for research-level mathematics text (i.e., scientific articles), which is our main focus of interest. The conventionality of this text gives rise to many opportunities for the application of NLP to MIR. In this paper, we investigate the role of mathematical types, a special kind of technical terminology. The term “type” refers to sequences of one or more words used to label mathematical objects (e.g., ‘set”, “smooth curve”), algebraic structures (e.g., “monoid”, “group”) and instantiable mathematical notions (e.g., “cardinality of a set”). Technical terms that are not used to refer to instances of these mathematical constructs are not types. Examples of non-types include references to the application of mathematical procedures (e.g., “proof by contradiction”) and elements of the mathematical discourse (e.g., “theorem 4.1”). As a subclass of mathematical terminology, types are almost exclusively noun or prepositional phrases. Types play a central role in communicating mathematical information by enabling mathematicians to name mathematical concepts, assign properties to objects and prove assertions about them. We consider types worthy of distinction from generic technical terms for two reasons: (a) types are used in the dis- course to give sense to constituents of formulae and (b) types are used to consistently evoke mathematical concepts in textual argumentation and mathematical reasoning. Our goal is to evaluate the usefulness of types as standalone lexical components in the retrieval of research-level mathematical information needs. Specifically, our hypothesis is twofold: (a) types are important discriminators in the mathematical discourse and (b) semantic relationships between types can be used to enrich queries and obtain significant improvements in retrieval efficiency. A sub-task of our type-based approach is the construction of a type dictionary from a collection of documents. We address this in section 3 and describe a simple method for automatic …

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