The Tangent Search Engine: Improved Similarity Metrics and Scalability for Math Formula Search
This addresses the need for robust and scalable mathematical information retrieval for users, including non-experts, who search by formula appearance, but it is incremental as it builds on existing retrieval methods.
The paper tackles the problem of searching for mathematical formulae on the web by developing a new similarity metric and scalable retrieval system, achieving state-of-the-art performance on the NTCIR-11 benchmark with efficient index space and retrieval time.
With the ever-increasing quantity and variety of data worldwide, the Web has become a rich repository of mathematical formulae. This necessitates the creation of robust and scalable systems for Mathematical Information Retrieval, where users search for mathematical information using individual formulae (query-by-expression) or a combination of keywords and formulae. Often, the pages that best satisfy users' information needs contain expressions that only approximately match the query formulae. For users trying to locate or re-find a specific expression, browse for similar formulae, or who are mathematical non-experts, the similarity of formulae depends more on the relative positions of symbols than on deep mathematical semantics. We propose the Maximum Subtree Similarity (MSS) metric for query-by-expression that produces intuitive rankings of formulae based on their appearance, as represented by the types and relative positions of symbols. Because it is too expensive to apply the metric against all formulae in large collections, we first retrieve expressions using an inverted index over tuples that encode relationships between pairs of symbols, ranking hits using the Dice coefficient. The top-k formulae are then re-ranked using MSS. Our approach obtains state-of-the-art performance on the NTCIR-11 Wikipedia formula retrieval benchmark and is efficient in terms of both index space and overall retrieval time. Retrieval systems for other graphical forms, including chemical diagrams, flowcharts, figures, and tables, may also benefit from adopting our approach.