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With the ever-increasing quantity and variety of data worldwide, the Web hasbecome a rich repository of mathematical formulae. This necessitates thecreation 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, thepages that best satisfy users' information needs contain expressions that onlyapproximately match the query formulae. For users trying to locate or re-find aspecific expression, browse for similar formulae, or who are mathematicalnon-experts, the similarity of formulae depends more on the relative positionsof symbols than on deep mathematical semantics.  We propose the Maximum Subtree Similarity (MSS) metric forquery-by-expression that produces intuitive rankings of formulae based on theirappearance, as represented by the types and relative positions of symbols.Because it is too expensive to apply the metric against all formulae in largecollections, we first retrieve expressions using an inverted index over tuplesthat encode relationships between pairs of symbols, ranking hits using the Dicecoefficient. The top-k formulae are then re-ranked using MSS. Our approachobtains state-of-the-art performance on the NTCIR-11 Wikipedia formularetrieval benchmark and is efficient in terms of both index space and overallretrieval time. Retrieval systems for other graphical forms, including chemicaldiagrams, flowcharts, figures, and tables, may also benefit from adopting ourapproach.

The Tangent Search Engine: Improved Similarity Metrics and Scalability for Math Formula Search