Multi-Stage Math Formula Search
Richard Zanibbi, Kenny Davila, Andrew W. Kane, Frank Wm. Tompa · 2016
When using a mathematical formula for search (query-by-expression), the suitability of retrieved formulae often depends more upon symbol identities and layout than deep mathematical semantics. Using a Symbol Layout Tree representation for formula appearance, we propose the Maximum Subtree Similarity (MSS) for ranking formulae based upon the subexpression whose symbols and layout best match a query formula. Because MSS is too expensive to apply against a complete collection, the Tangent-3 system first retrieves expressions using an inverted index over symbol pair relationships, ranking hits using the Dice coefficient; the top-k formulae are then re-ranked by MSS. Tangent-3 obtains state-of-the-art performance on the NTCIR-11 Wikipedia formula retrieval benchmark, and is efficient in terms of both space and time. Retrieval systems for other graphical forms, including chemical diagrams, flowcharts, figures, and tables, may benefit from adopting this approach.