Layout-Based Substitution Tree Indexing and Retrieval for Mathematical Expressions

摘要

We introduce a new system for layout-based (LaTeX) indexing and retrieval of mathematical expressions using substitution trees. Substitution trees can efficiently store and find expressions based on the similarity of their symbols, symbol layout, sub-expressions and size. We describe our novel implementation and some of our modifications to the substitution tree indexing and retrieval algorithms. We provide an experiment testing our system against the TF-IDF keyword-based system of Zanibbi and Yuan and demonstrate that, in many cases, the quality of search results returned by both systems is comparable (overall means, substitution tree vs. keyword-based: 100% vs. 89% for top 1; 48% vs. 51% for top 5; 22% vs. 28% for top 20). Overall, we present a promising first attempt at layout-based substitution tree indexing and retrieval for mathematical expressions and believe that this method will prove beneficial to the field of mathematical information retrieval.