A Structure Based Approach for Mathematical Expression Retrieval

摘要

Mathematical expression (ME) retrieval problem has currently received much attention due to wide-spread availability of MEs on the World Wide Web. As MEs are two-dimensional in nature, traditional text retrieval techniques used in natural language processing are not sufficient for their retrieval. In this paper, we have proposed a novel structure based approach to ME retrieval problem. In our approach, query given in $mbox{LaTeX}$ format is preprocessed to eliminate extraneous keywords (like displaystyle, egin{array} etc.) while retaining the structure information like superscript and subscript relationships. MEs in the database are also preprocessed and stored in the same manner. We have created a database of 829 MEs in $mbox{LaTeX}$ form, that covers various branches of mathematics like Algebra, Trigonometry, Calculus etc. Preprocessed query is matched against the database of preprocessed MEs using Longest Common Subsequence (LCS) algorithm. LCS algorithm is used as it preserves the order of keywords in the preprocessed MEs unlike bag of words approach in the traditional text retrieval techniques. We have incorporated structure information into LCS algorithm and proposed a measure based on the modified algorithm, for ranking MEs in the database. As proposed approach exploits structure information, it is closer to human intuition. Retrieval performance has been evaluated using standard precision measure.