A lattice-based approach for mathematical search using Formal Concept Analysis

Abstract

Mathematical (or math) search is a challenging problem as math expressions are highly symbolic and structured. The vast majority of math search systems that adopt conventional text retrieval techniques are ineffective in searching math expressions. In this paper, we propose a lattice-based approach for math search. The proposed approach is based on Formal Concept Analysis (FCA), which is a powerful data analysis technique. In the proposed approach, math expressions are first converted into the corresponding MathML representation, from which math features are extracted. Next, the extracted features are used to construct a mathematical concept lattice. At the query time, the query expression is processed and inserted into the mathematical concept lattice, and the relevant expressions are retrieved and ranked. Finally, search results can be visualized and nevigated via a dynamic graph, thanks to the lattice structure. The proposed lattice-based math search approach is benchmarked against a conventional best match retrieval technique and results show it to be almost 10% better in terms of F1 for the top 30 retrieved results.