Layout and Semantics: Combining Representations for Mathematical Formula Search

摘要

Math-aware search engines need to support formulae in queries.rnMathematical expressions are typically represented as trees de€ningrntheir operational semantics or visual layout. We propose searchingrnboth formula representations using a three-layer model. Œe €rstrnlayer selects candidates using spectral matching over tree nodernpairs. Œe second layer aligns a query with candidates and computesrnsimilarity scores based on structural matching. In the thirdrnlayer, similarity scores are combined using linear regression. Œerntwo representations are combined using retrieval in parallel indicesrnand regression over similarity scores. For NTCIR-12 WikipediarnFormula Browsing task relevance rankings, we see each layer increasingrnranking quality and improved results when combiningrnrepresentations as measured by Bpref and nDCG scores.